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1-1: Words and Expressions

1. Numerical expressions contain a combination of numbers and operations

such as addition, subtraction, multiplication, and division.

2. Evaluate- find its numerical value

3. Order of operations- the rules to follow when evaluating an expression with

More than one operation

4. Order of Operations:

A. Work inside grouping symbols first

B. Multiply and/or divide in order from left to right

C. Add and/or subtract in order from left to right

5. Look at the examples on pages 5-7.

1-2: Variables and Expressions

1. Algebra- a branch of mathematics that uses symbols

2. Variable- a letter or symbol used to represent an unknown value

3. Algebraic expression- an expression that contains at least one variable and at

least one mathematical expression (add, subtract, multiply, or divide)

4. Defining a variable- to choose a variable and quantity for the variable to

represent

5. Substitution Property of Equality- when you replace a variable with a number

(if the two quantities are equal, then one quantity can be replaced by the

other)

6. To write an algebraic expression:

A. Describe the situation using only the most important words

B. Define a variable

C. Translate your verbal model into an algebraic expression

7.

+ - X ÷

Increased Decreased Product quotient

More than Less than Times Divided

Sum Difference Each per

Plus Minus Multiply

Add Subtract Per

Total


1-3: Properties

1. Properties- statements that are true for any numbers

2. Commutative Property of Addition- states that the order in which numbers are

added does not change the sum

For any numbers a and b a+b=b+a

6 and 9 6+9=9+6

3. Commutative Property of Multiplication- states that the order in which

numbers are multiplied does not change the product

For any numbers a and b ab=ba

4 and 7 4×7=7×4

4. Associative Property of Addition-states that the order in which numbers are

grouped when added does not change the sum

For any numbers a, b, and c (a+b)+c=a+(b+c)

3, 6, and 1 (3+6)+1=3+(6+1)

5. Associative Property of Multiplication- states that the order in which numbers

are grouped when multiplied does not change the product

For any numbers a, b, and c (ab)c=a(bc)

3, 6, 1 (3×6)×1=3×(6×1)

6. Draw the Key Concept table on page 19.

7. Counterexample-an example that shows a conjecture (statement) is not true

8. Simplify-perform all possible operations (work as much as you can)

9. Deductive reasoning- using facts, properties, or rules to reach conclusions.

10.Look at the examples on pages 19-20.

1-4: Ordered Pairs and Relations

1. Coordinate plane (coordinate system)- is formed by the intersection of 2

number lines that meet at right angles at their zero points

2. Y-axis - the vertical number line in a coordinate plane

3. X-axis - the horizontal number line in a coordinate plane

4. Origin (0,0)- the point at which the number lines intersect

5. Ordered pair- a pair of numbers that tell the location of a point on a

coordinate plane

6. X-coordinate - the 1st number listed in an ordered pair

7. Y-coordinate - the 2nd number listed in an ordered pair

8. Graph(an ordered pair)- to draw a dot at the point that corresponds to the

ordered pair

9. Relation- a set of ordered pairs

10.Domain- the x-coordinate in a relation

11.Range- the y-coordinate in a relation y-coordinate

Quadrant II Quadrant I

12.

Quadrant III Quadrant IV

x-coordiate


1-5: Words, Equations, Tables, and Graphs

1. Function-a relation in which each member of the domain is paired with exactly

one member in the range

2. Function table- the operation(s) performed on the domain value to get the

range value (what you do to the domain to get the range)

3. Function table- a table that lists the x-coordinate (input), rule, and y-value

(output)

4. Equation- a mathematical sentence stating that two quantities are equal


1-6: Scatter Plots

1. Scatter plot- shows the relationship between a set of data with two variables,

graphed as ordered pairs on a coordinate plane

2. Positive relationship- the data appears to rise as it goes to the right (as x

increases the y increases)

3. Negative relationship- the data appears to fall as it goes to the right (as x

increases the y decreases)

4. No relationship- the data is so scattered there is no pattern



2-1: Integers and Absolute Value

1. Negative number- a number less than zero

2. Positive number- a number greater than zero

3. Integers- the whole numbers and their opposites

Ex. …-4, -3, -2, -1, 0, 1, 2, 3, 4 … …means continues indefinitely

4. Coordinate- the number that corresponds to the point on a number line (look

at the sample at the top of page 62).

5. Inequality- a mathematical sentence that contains <, >, ≤, ≥ or ≠.

6. Remember the farther left a number is on a number line, the smaller the

number is.

7. Absolute value- the distance a number is from zero on a number line (it does

not matter if you must go left or right)

8. Look at the problems 38, 39, and 40 on page 65. The lines around the

numbers are absolute value bars.


2-2: Adding Integers

1. Opposites- the numbers with the same absolute value but different signs

Ex. 5 and -5 -7 and 7 -a and a

2. Additive inverse- an integer and its opposite

3. To add integers with the same sign:

A. Ignore the signs and just plain add

B. Put the same sign (that both integers had) on the answer

4. Look at the examples on page 70.

5. To add integers with different signs:

A. Ignore the signs and subtract

B. Now decide which number has the greater absolute value and put its sign

on your answer.

6. Look at the examples on page71.

2-3: Subtracting Integers

1. To subtract an integer, add its additive inverse.

2. To subtract an integer:

A. Change the subtraction sign to an addition sign

B. Make the number to the right its opposite

C. Now follow the rules listed in lesson 2-2 note #3 and #4.


2-4: Multiplying Integers

1. To multiply integers with different signs:

A. Ignore the signs and just plain multiply

B. Put a negative sign on your answer

2. To multiply integers with the same sign:


B. The answer is positive so no sign on your answer is necessary

3. To multiply integers:


B. If the signs on your integers are different the answer is negative

C. If the signs on your integers are the same the answer is positive

D. Look at the examples on pages 83-85.

2-5: Dividing Integers

1. Mean(average)- to find the average, find the sum of the numbers and then

divide the number of items in the set

2. To divide integers with different signs:

A. Ignore the signs and just plain divide

B. The signs are different so the answer is negative

3. To divide integers with the same signs:

A. Ignore the signs and just plain divide.

B. The signs are the same so the answer is positive

4. To divide integers:

A. Ignore the signs and just plain divide

B. If the signs on your integers are different the answer is negative

C. If the signs on your integers are the same the answer is positive


6. Study the Concept Summary table on page 92.

2-6: Graphing in Four Quadrants

1. Quadrants- the four regions that the x-axis and the y-axis separate the

coordinate plane into (look back at note section 1-4)

2. Remember to list the x-coordinate first and then the y-coordinate

3. Remember to write the quadrant number as a roman numeral.


2-7: Translations and Reflections on the Coordinated Plane

1. Transformation- a movement of a geometric figure

2. Image-every corresponding point on a figure after its transformation (the

picture you get after a transformation)

3. Translation- a transformation when a figure is slid from one position to

another without being turned. Also called a slide.

4. Reflection-a transformation when a figure is flipped over a line. Also called a

flip

5. Line of symmetry- a line over which a reflection is flipped

6. A translation:

A. Called a slide

B. The image is the same size and shape as the original figure

C. Orientation is the same as the original figure

7. A reflection:

A. Called a flip

B. The image is the same size and shape as the original figure

C. Orientation is the same as the original figure


3-1: Fractions and Decimals

1. Terminating decimal-a decimal that stops (the remainder is 0)

2. Repeating decimal- decimals that repeat with a pattern without end

3. Bar notation- a bar or line placed over the digit(s) that repeats

4. To write a fraction as a decimal divide the numerator by the denominator

(the # on top goes in the box)

5. Draw the Concept Summary chart on the bottom of page 122.


3-2: Rational Numbers

1. Rational numbers- any number that can be written as a fraction

2. Rational numbers include:

A. Whole numbers

B. Integers

C. Terminating decimals

D. Repeating decimals (repeat with a pattern)

E. Fractions

F. Mixed numbers

3. To write a mixed number or integer as a fraction:

A. Write the mixed number or integer as an improper fraction

Denominator times whole number plus the numerator

Same denominator

OR

PUT THE INTEGER OVER 1

4. To write a decimal as a fraction:

A. Read the decimal properly

B. Write what you read

C. Reduce if possible

5. To write a repeating decimal as a fraction:

A. First set the repeating decimal equal to N

B. Then decide how many digit repeat

C. If 1 digit repeats multiply each side by 10 ( if 2 digits repeat multiply each

side by 100 and so on)

D. Now subtract

E. Now solve the equation


7. Draw the Concept Summary chat on page 130.

3-3: Multiplying Rational Numbers

1. To multiply fractions:

A. Multiply the numerators

B. Multiply the denominators

C. Reduce if possible

2. To multiply mixed numbers make them improper first then follow note

number 1.


3-4: Dividing Rational Numbers

1. Multiplicative inverse (reciprocal)- two numbers whose product is 1

2. To find a multiplicative inverse (reciprocal) of a fraction, just flip the

fraction over.

3. To find a multiplicative inverse (reciprocal) of a mixed number:

A. Make the mixed number an improper fraction

B. Now flip the improper fraction

4. To find a multiplicative inverse (reciprocal) of a whole number:

A. Make the whole number a fraction by putting it over 1

B. Now flip the fraction

5. To divide by a fraction, multiply by its multiplicative inverse (reciprocal)

6. To divide fractions:

A. Flip the 2 nd fraction, never the first, and multiply


3-5: Adding and Subtracting Like Fractions

1. Like fractions- fractions with the same denominator

2. To add fractions with like denominators:

A. Add the numerators (the numbers on top)

B. Write this sum over the denominator (you do not add the denominators)

3. To add mixed numbers:

A. Make the mixed numbers improper fractions

B. Now follow the rules in note #2

4. To subtract fractions with like denominators:

A. Subtract the numerators (the numbers on top)

B. Write this difference over the denominator (you do not subtract the

denominators)

5. To subtract mixed numbers:

A. Make the mixed numbers improper fractions

B. Now follow the rules in note #4


3-6: Adding and Subtracting Unlike Fractions

1. Unlike fractions- fractions with different denominators

2. To add fractions with unlike denominators:

A. Rename the fractions with a common denominator

B. Follow the rules from lesson 3-5

3. To add fractions and mixed numbers with unlike denominators:

A. Make the mixed numbers improper

B. Now follow note #2

4. To subtract fractions with unlike denominators:

A. Rename the fraction with a common denominator

B. Follow the rules from lesson 3-5

5. To subtract fractions and mixed numbers with unlike denominators:

A. Make the mixed numbers improper

B. Now follow note #4


4-1: The Distributive Property

1. Equivalent expressions- expressions that have the same value

2. Distributive Property- to multiply a sum or difference by a number, multiply

each term inside the parentheses by the number outside the parentheses



4-2: Simplifying Algebraic Expressions

1. Term-each part that an addition or subtraction sign divides an algebraic

expression into

2. Coefficient- the numerical part of a term that contains a variable

3. Like terms-terms that contain the same variable (or no variable at all)

4. Constant-a term without a variable

5. Simplest form- when an expression has no like terms and no parentheses

6. Simplifying the expression-when you use the Distributive Property to combine

like terms.

7. Look at the instructions in the middle of page 178.


4-3: Solving Equations by Adding or Subtracting

1. Equation- a mathematical sentence that contains an equal sign

2. Solution- a value for a variable that makes an equation true

3. Solving the equation- the process of finding a solution

4. Inverse operations-“undo” each other (ex. Addition and subtraction

Multiplication and division)

5. Equivalent equation- equations that have the same solutions

6. Addition Property of Equality- If you add the same number to each side of an

equation, the two sides remain equal

7. Subtraction Property of Equality-If you subtract the same number from each

side of an equation, the two sides remain equal

8. To solve addition equations:

A. Put a dashed line through the equal sign

B. Ask yourself what number is on the same side as the variable

C. Put the opposite under this number and also put it on the other side of the

dashed line

D. Now just do the math

9. To solve subtraction problems:


B. Change the subtraction sign to addition and make the number to the right

of the subtraction sign its opposite.

C. Ask yourself what number is on the same side as the variable?

D. Put the opposite under this number and also put it on the other side of the

dashed line.

E. Now just do the math

4-4: Solving Equations by Multiplying or Dividing

1. Division Property of Equality- When you divide each side of an equation by the

same nonzero number, the two sides remain equal

2. To solve multiplication equations:



C. Divide each side by this exact same number


3. Multiplication Property of Equality- When you multiply each side of an

equation by the same nonzero number, the two sides remain equal

4. To solve division equations:

A. Put a dashed line through the equal sign.


C. Multiply each side by this exact same number


4-5: Solving Two-Step Equations

1. Two-step equations- an equation that contains 2 steps

2. To solve two-step equations:


B. Make sure you have an addition sign

C. Ask yourself what 2 numbers are on the same side as the variable

D. Now ask yourself with number is physically farther from the variable (work

with this number first)

E. Put the opposite of this number underneath it and also put it on the other

side of the dashed line.

F. Do the math and bring everything else straight down.

G. Ask yourself what number is on the same side as the variable

H. If the problem says multiply divide by this exact number (on both sides of

the equal sign).

I. If the problem says divide multiply by this exact number (on both sides of

the equal sign).

4-6: Writing Equations

1. Refer to note section 1-2 note #7.

2. Remember is means to put an equal sign.


5-1: Perimeter and Area

1. Formula- an equation that shows a relationship among certain quantities

2. Perimeter- the distance around a geometric figure3. Area- the measure of the surface enclosed by a figure4. The perimeter of a rectangle is the sum of twice the length and twice the

width (or just add up all the sides)P= 2L + 2w or P= 2(L+w) or P=L+w+L+w

5. The perimeter of a triangle is the sum of the measures of all three sides (just add up all the sides)P= a+b+c

6. The area of a rectangle is the product of the length and width (length times width).A= L × w or A=Lw

7. The area of a triangle is one-half the product of the base and height.A=1/2bh

8. Make sure when finding the area you write your answers in square units.9. Look at the examples on pages 221-223.

5-2: Solving Equations with Variables on Each Side

1. To solve equations with variables on each side:

A. First you must get the variables on the same side (never move the variable that is by itself)

B. To move a coefficient and a variable at the same time, put the opposite underneath it and also put it on the other side of the dashed line.

C. Now do the math.D. Now the problem is just an equation. Solve just like you did in lessons 4-3,

4-4, and 4-5.2. Look at the examples on pages 229-230.

5-3: Inequalities

1. Inequality- a mathematical sentence that compares quantities that are not equal using the symbols <, >, ≥, ≤.

2. Use the following table to write inequalities:

< > ≤ ≥Less than Greater than Less than or equal to Greater than or equal to

Fewer than More than No more than No less thanExceeds At most At

3. Inequalities with variables are open sentences.4. When the variable in an open sentence is replaced with a number, the

inequality may be true or false.5. To graph an inequality:

A. Make sure the variable is on the left hand sideB. Make an arrow out of the inequality symbolC. Find the number on a number line and circle the mark on the number line

above it.D. Look to see if the inequality had an or equal to mark (a line under the

symbol)E. If it does color in the circleF. If it does not do not color in your circleG. Now graph the direction your arrow points (the arrow you made in step B)

6. To write an inequality from a graph:A. Begin by just writing down a variableB. Check to see if the circle is colored inC. If the line is shaded to the left use this symbol <D. If the line is shaded to the right use this symbol >E. If the circle is colored in put an “or equal to” markF. Finally write down the number that is graphed


5-4: Solving Inequalities

1. Solve these problems just as you solved the problems in lessons 4-3 and 4-4.2. When solving inequalities, make sure the variable is on the left hand side.3. If the variable is not on the left hand side, you must flip the problem and the

symbol.4. IMPORTANT—When multiplying or dividing if the number next to the variable

is negative you must flip the symbol.5. Look at the examples on pages 241-244.

5-5: Solving Multi-Step Equations and Inequalities

1. Null or empty set- when an equation has no solution2. Identity- an equation that is true for every value of the variable3. Solve these problems just like lesson 4-5 and 5-2, but you may have to use the

Distributive Property (lesson 4-1) first.4. Look at the examples on pages 248-250.

6-1: Ratios

1. Ratio- a comparison of two numbers by division2. You can write ratios 3 ways:

3:1 3 to 1 3/13. Look at the examples on pages 265-266.

6-2: Unit Rates

1. Rate- a ratio of two quantities having different kinds of units2. Unit rate-when a rate is simplified so that it has a denominator of 13. Divide the numerator by the denominator to get the unit rate (the 1st number

by the second).4. To find a unit price money always goes inside the division box.5. Look at the examples on pages 270-271.

6-3: Converting Rates and Measurements

1. Dimensional analysis- the process of including units of measurement as factors when you compute

2. Draw the Key Concepts table on page 276.3. Look at the examples on pages 275-277.4. When using the customary system if you go from a little unit to a big unit

multiply by the conversion factor.5. When using the customary system if you go from a big unit to a little unit

divide by the conversion factor.6. When changing between the metric and customary systems multiply by the

conversion factor.

6-4: Proportional and Nonproportional Relationships

1. Proportional- two quantities that have a constant ratio or rate (two ratios are proportional if they are equal)

2. Nonproportional- two quantities that do not have a constant ratio or rate3. (two ratios are nonproportional if they are not equal)4. Constant of proportionality- a constant ratio or unit rate of a proportion5. Look at the examples on pages 280-282.

6-5 Solving Proportions

1. Proportion- an equation stating that two ratios or rates are equal2. Cross products; if a/c=b/d then ad=bc. If ad=bc the a/c=b/d

(multiply across diagonally) and makes a proportion3. Property of Proportions- the cross products of a proportion are equal4. To solve a proportion:

A. Look across diagonally and multiply the two numbersB. Now divide that product by the number you haven’t used yet.

5. When writing a proportion you must keep the proportion balanced (what is on top on the left side must be on top on the right side; what is on the bottom on the left side must be on bottom on the right side.


6-6: Scale Drawings and Models

1. Scale drawing or scale model- are used to represent an object that is too large or too small to be drawn or built at actual size

2. The length and widths of objects on a scale drawing or model are proportional to the lengths and widths of the actual object.

3. Scale- a ratio of a given length on the drawing or model to its corresponding length on the actual object.Remember: scale/actual= scale/actual

4. Scale factor- the ratio of a length on a scale drawing or model to the corresponding length on the real object


6-7: Similar Figures

1. Similar figures- figures that have the same shape but not necessarily the same size

2. Corresponding parts- parts of congruent or similar figures that match3. Congruent- have the same measure (equal)4. If two figures are similar:

A. The corresponding angles are congruent (have the same measure)B. The corresponding sides are proportional

5. Look at the small print under the Key Concept table on page 301.6. Look at example 1 on page 302 to see the similar symbol ( it looks like a single

squiggly line). 7. Look at the examples on pages 302-303.

6-8: Dilations

1. Dilation- a transformation that enlarges or reduces a figure by a scale factor2. In a translation you slide the figure.3. In a reflection you flip the figure.4. In a dilation you shrink or enlarge a figure.5. When the center of a dilation is the origin, you can find the coordinates of the

image by multiplying each coordinate of the figure by the scale factor.6. A dilation with a scale factor of k will be:

A. An enlargement if k>1B. A reduction if 0<k<1C. The same as the original figure if k=1


6-9: Indirect Measurement

1. Indirect measurement- when you use the properties of similar triangles to find measurements that are difficult to measure directly (use Little-Big Little-Big)


7-1: Fractions and Percents

1. Percent- is a ratio that compares a number to 1002. A percent is a part to whole ratio that compares a number to 100.3. To write a percent as a fraction just write it over 100.4. To write a fraction as a percent et the denominator equal to 100 . The write

the fraction as a percent.5. If you cannot write the denominator equal to 100, divide the numerator by

the denominator, get a decimal then move the decimal 2 places to the right and add a percent sign.

6. Another method is to set up a proportion.7. Look at the examples on pages 331-333.

7-2: Fractions, Decimals, and Percents

1. To write a percent as a decimal, divide by 100 and remove the percent sign(move the decimal 2 places to the left and remove the percent sign).

2. To write a decimal as a percent, multiply by 100 and add a percent sign (move the decimal 2 places to the right and add a percent sign).

3. To write a fraction as a percent divide the numerator by the denominator (top by bottom: top number goes in the division box the bottom number goes outside the division box).

4. To compare percents, decimals and fractions, convert them all to the same form and then compare.

5. Draw the Concept Summary table at the bottom of page 339.

7-3: Using the Percent Proportion

1. Percent proportion- part/whole=%/1002. In a word problem the whole follows the word of.3. Look at the examples on pages 345-347.

7-4: Find Percent of a Number Mentally

1. Draw and memorize the table on page 351.2. Look at the examples on pages 351-353.

7-5: Using Percent Equations

1. Percent equation- an equivalent form of the percent proportion in which the percent is written as a decimal

2. Is means =3. Of means multiply4. Look at the examples on pages 357-359.

7-6: Percent of Change

1. Percent of change- a ratio that compares the change in quantity to the original amount

2. Percent of increase- when the percent is positive3. Percent of decrease- when the percent is negative4. Markup- the amount of increase5. Selling price- the amount the customer pays for an item6. Discount- the amount by which the regular price is reduced7. Percent of change= amount of change

Original amount8. To find the percent of change:

A. Subtract the two amountsB. Divide this difference by the original amount

9. To find the selling price:(markup)A. Figure the markup (multiply the markup rate by the original price)B. Add the markup from the original price

10.To find the selling price: (markup)A. Add the markup rate to 100%.B. Now multiply this new percent times the original price.

11.To find the selling price: (discount)A. Figure the discount (multiply the discount rate by the original price)B. Subtract the discount from the original price.

12. To find the selling price: (discount)A. Subtract the discount rate from 100%.B. Now multiply this new percent times the original price.

7-7: Simple and Compound Interest

1. Interest- the amount of money paid or earned for the use of money by a bank or other financial institution.

2. Simple interest- interest paid only on the initial principal of a savings account or loan

3. Principal- the amount of money invested or borrowed4. Compound interest- interest paid on the initial principal and on the interest

earned in the past.5. Look at the formula in the middle of page 370 (it is in different colored ink).6. Look at the examples on pages 380-371.

7-8 Circle Graphs

1. Circle graph (pie graph)- a graph used to compare parts of a data set to the whole set of data

2. There are 360 degrees in a circle.3. To find out how many degrees each part of your circle graph should be,

multiply your percent by 360.4. Look at the examples on pages 376-378.

8-1 Functions

1. independent variable- the variable in a function with a value that is subject to change

2. dependent variable- the variable in a relation with a value that depends on the value of the independent variable

3. REMEMBER…the domain is the 1st coordinate.4. REMEMBER…the range is the 2nd coordinate.5. In a function each member of the domain is paired with exactly one

member of the range.6. It is OK for there to be 2 domains with 1 range, but there cannot be 2

different ranges with 1 domain.7. Vertical Line Test-if you have a vertical line and it passes through two or

more points on the graph (at the same time) it is NOT a function.8. Function notation- a way to name a function that is defined by an equation

(ex. Equation y=3x-8 Function Notation f(x)=3x-8 )9. To find a function value: Plug in the number in the place of the variable.10. Examples

8-2 Sequence and Equations

1. Sequence- an ordered list of numbers

2. Term- each number in the sequence3. Arithmetic Sequence- when the difference between any two consecutive

terms is the same4. Common Difference- this is the difference in the arithmetic sequence5. Begin explanations with… The terms have a common difference of ______.

A term is _____ (more than or times) the previous term number.6. Examples

8-3 Representing Linear Functions

1. Linear equation- an equation whose graph is a line.

2. X-intercept- where the point crosses the X axis (X, 0)3. Y-intercept- where the point crosses the Y axis (0, Y)4. To graph a line from an equation:

A. Find the X-intercept (Plug in 0 for Y and solve)B. Graph the ordered pairC. Find the Y-intercept (Plug in 0 for X and solve)D. Graph the ordered pairE. Connect the points with a line

5. Examples

8-4 Rate of Change

1. Rate of change- a rate that describes how one quantity changes in relation to another quantity

2. To find a rate of change find the …. Change in y

Change in x

3. On a graph the vertical axis is the Y and the horizontal axis is the X.4. Draw the table on page 414.5. Examples

8-5 Constant Rate of Change and Direct Variation

1. Linear relationship- a relationship that has a straight-line graph.2. Constant rate of change- when the rate of change between any two data

points in a linear relationship are the same or constant.3. Direct Variation- when the ratio of two variable quantities is constant4. A constant rate of change will be a straight line (can be slanted but not

curved).5. Examples

8-6 Slope

1. Slope- the ratio of the rise-vertical change to the run-horizontal change of a line (the slant of a line)

2. Slope= rise run

3. To find the slope of a line using a graph:A. Pick two points on a lineB. Find the rise (up and down)C. Find the run (left and right)D. Put the rise over the run

4. If the line goes up from left to right the slope is positive.5. If the line goes down from left to right the slope is negative6. If the line is horizontal the slope is 0.7. If the line is vertical the slope is undefined.8. To find the slope of a line using ordered pairs:

A.Label the ordered pairs

B. Use the following formula

C. Do the Math

9. If you subtract and get 0 on top the slope is 0.

10. If you subtract and get 0 on bottom the slope is undefined.

11. Examples

8-7 Slope-Intercept Form

1. Slope-intercept from- an equation in the form Y=mX + b, where m=slope and b=the Y intercept

2. In slope-Intercept form Y must be by itself and must be positive.3. To graph an equation using the slope and Y- intercept :

A. Always graph the Y intercept firstB. Then if the slope is not a fraction make it a fractionC. Now use this fraction to graph rise

Run4. Examples

8-8 Writing Linear Equations

1. Point-slope form- an equation in the form: Y-Y subscript of 1= m(X-X subscript of 1) where n represents the slope and (X subscript of 1, Y subscript of 1) represents a point on the line.

2. One way to write a linear equation is to substitute the values for the slope and y-intercept.

3. To write an equation from two given points:A. Find the slopeB. Use the slope and the coordinates of either point to write the equation

in point-slope form.4. To write an equation from a table:

A. Find the slopeB. Use the slope and the coordinates of either point to write the equation

in point slope form.5. Draw the table on the top of page 444.6. Examples

8-9 Predicting Equations

1. Line of fit- a line that is very close to most of the data points

2. To make a prediction from a line of fit:A. Graph the data in a scatter plotB. Draw a line of fitC. Make your prediction based on the line (extend the line if necessary)

3. Examples

8-10 Systems of Equations

1. System of equations-a collection of 2 or more equations with the same set of variables

2. One way to solve a system of equations is to graph the equations on the same coordinate plane. The point at which the two lines cross is the solution of that system.

3. Draw the concept summary table on page 455.4. Substitution-an algebraic method to solve systems where you substitute a

number for a variable.5. Examples

Date post:	07-Mar-2018
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s3. Web viewInequalities with variables are open sentences. ... When solving inequalities, make...

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