LLesson 4.3 Graphing Linear Equations ESSON 4.3 GRAPHING L EQUATIONS · · 2017-07-27linear...

214 Chapter 4 Linear Equations

Lesson 4.3 Graphing Linear EquationsObjectives Graph linear equations. Identify the slope and

y-intercept of linear equations.

Suppose a baker’s cookie recipe calls for a mixture of nuts, raisins, and dried fruit. Some customers prefer lots of nuts; others would rather have more raisins. The recipe states that whichever way you mix them, when you add the number of cups of raisins to the number of cups of nuts, and then add this to

4.4 Graphing Linear Equations 225

Suppose a baker’s cookie recipe calls for a mixture of nuts, raisins,and chocolate chips. Some customers prefer lots of nuts; otherswould rather have more raisins. The recipe states that whicheverway you mix them, when you add the number of cups of raisins tothe number of cups of nuts, and then add this to

34

cup of chocolatechips, you must have a total of 3 cups. How can you write anequation to model this situation? How would you draw the graph?

The equation y 2x expresses a relationship between twovariables x and y. In this relationship, the value of y depends on thevalue that is substituted for x. Thus, x is called the independentvariable and y is called the dependent variable. If you select 1 asthe value of the independent variable x, then 2 is the value of thedependent variable y.

Graph the equation y 2x. How does the graph compare to thegraph of y x?

The equation y 2x is solved when you find the ordered pairs thatmake the equation a true statement. One solution of the equation isthe ordered pair (1, 2). Because the solution of y 2x is a set ofordered pairs, a table of values or a graph can represent y 2x.

In a table, the first column is usually labeled as the independentvariable. The second column is labeled as the dependent variable.Because you cannot list all the ordered pairs that make the equationa true statement, three to five pairs are usually enough. From thetable, it can be seen that for each increase in x, y increases by 2.Therefore the slope of the equation is 2.

EXAMPLE 1 GRAPHING A LINEAR EQUATION

Graph Linear Equations

LESSON 4.3 GRAPHING LINEAR EQUATIONS

OBJECTIVESGraph linear equations.Identify the slope and y-intercept of linear equations.

x y1 20 0

1 22 4

cup of dried fruit, you must have a total of 3 cups. How can you write an equation to model this situation? How would you draw the graph?

Graph Linear Equations

The equation y 2x expresses a relationship between two variables x and y. In this relationship, the value of y depends on the value that is substituted for x. Thus, x is called the independent variable and y is called the dependent variable. If you select 1 as the value of the independent variable x, then 2 is the value of the dependent variable y.

Example 1 Graphing a Linear Equation

Graph the equation y 2x. How does the graph compare to the graph of y x?

Solution

The equation y 2x is solved when you find the ordered pairs that make the equation a true statement. One solution of the equation is the ordered pair (1, 2). Because the solution of y 2x is a set of ordered pairs, a table of values or a graph can represent y 2x.

In a table, the first column is usually labeled as the independent variable. The second column is labeled as the dependent variable. Because you cannot list all the ordered pairs that make the equation a true statement, three to five pairs are usually enough.

x y

1 2

0 0

1 2

2 4

From the table, it can be seen that for each increase in x, y increases by 2. Therefore the slope of the equation is 2.


After you complete the table, graph each pair of (x, y) values as a point. Draw the line that passes through all the points. Then graph the parent function y x on the same coordinate plane.

1–1

1

2

3

4

5

6y

–1

–2

–3

–4

–5

–6

–2–3–4–5–6 2 3 4 5 6

x

y = 2x

y = x

0

Examine the figure that shows the graphs of y 2x and y x on the same pair of axes. Because the graphs are straight lines, y 2x and y x are called linear equations. Because the graph of the equation is determined by the table, you can find the slope of y 2x from the table.

Critical Thinking Explain how to use the table to find the slope of the linear equation y 2x.

Activity 1 The Slope of a Line

1 Use a table to graph each of the three equations on the same coordinate axes. Use four ordered pairs for each table.

a. y x b. y 3x c. y 5x

2 Use the slope formula to determine the slope of each line. Compare the slope of each line to the coefficient of the independent variable. What do you notice?

3 Guess the slope of y 6x. Use a table to check your guess.

Notice that the graph of each equation is a straight line that passes through the origin.

Critical Thinking Let m represent the slope of a line that passes through the origin. What is the equation of the line?

Example 2 Negative Slope

Compare the slope of y 2x with the slope of y 2x. Then compare each graph to the parent function y x.

Solution

Make a table of values and graph y 2x. First, choose four values for x. Then, use the equation to find the values for y.

After you complete the table, graph each pair of (x, y) values as a point. Draw the line that passes through the points. Write the equation along the line.

The steepness of these two lines is the same. However, they rise in opposite directions. Notice that the slopes are opposites.

Graph the parent function. The graph of y 2x is steeper than the graph of y x. The graph of y 2x is steeper and rises in the opposite direction as y x.

Positive and Negative SlopeA line that rises to the right has a positive slope. A line that rises to the left has a negative slope.

Look at your table of values for y 2x. Notice that as x increases in value, y decreases. In this case, the graph of the equation has a negative slope.

Critical Thinking In Example 2, do you need to graph all four ordered pairs to draw the line through them? What is the least number of points you need in order to draw the line that contains the point? Name a reason why you would graph more points.

x y

1 2

0 0

1 2

2 4

1–1

1

2

3

4

5

6y

–1

–2

–3

–4

–5

–6

–2–3–4–5–6 2 3 4 5 6

x

y = 2x

y = x

y = –2x

SW17216/Cord AlgebraFigure 5.38.TA

0


Activity 2 The y-intercept

1 Make tables of values and draw the graphs of these four equations on the same coordinate plane.

a. y 2x b. y 2x 1 c. y 2x 3 d. y 2x 2

2 What is the slope of each line?

3 Where does each line cross the y-axis?

4 Where does the graph of y 2x 5 cross the y-axis?

Slope-Intercept Form of an Equation

The y-value of the point where the line crosses the y-axis is called the y-intercept. The equation y 2x 5 is written in slope-intercept form. The slope is 2, and the y-intercept is (0, 5).

Slope-Intercept Form of a Linear Equationy mx b is a linear equation. The slope is m and the y-intercept is b. The line crosses the y-axis at the point (0, b).


Graph the equation 2y 3x 6 using slope-intercept form.

Solution

Write the equation in slope-intercept form. Solve the equation for y.

Make tables of values and draw the graphs of these fourequations on the same coordinate plane.

a. y 2x b. y 2x 1 c. y 2x 3 d. y 2x 2

What is the slope of each line?

Where does each line cross the y-axis?

Where does the graph of y 2x 5 crosses the y-axis?

The y-value of the point where the line crosses the y-axis is called they-intercept. The equation y 2x 5 is written in slope-interceptform. The slope is 2, and the y-intercept is 5.

Slope-Intercept Form of a Linear Equationy mx b is a linear equation. The slope is m and they-intercept is b. The line crosses the y-axis at the point(0, b).



2y 3x 6 Given

122y

12(3x 6) Multiplication Property of Equality

y 32x 3 Distributive Property and Simplify

The slope is 32

, and the linecrosses the y-axis at (0, 3).

Now draw the coordinate axes. Graph the y-intercept (0, 3) as onepoint on the line. Since the slope is

23, you can find another point

by moving up 3 and to the left 2. Locate that point. Connect the twopoints with a line.

SOLUTION

EXAMPLE 3 Graphing a Linear Equation


4

3

2

1

The y-intercept see marginACTIVITY 2

y

x

(0, 3)

(2, 6)

y = – x + 332

Now draw the coor dinate axes. Graph the y-intercept (0, 3) as one point on the line. The slope is

Make tables of values and draw the graphs of these fourequations on the same coordinate plane.

a. y 2x b. y 2x 1 c. y 2x 3 d. y 2x 2

What is the slope of each line?

Where does each line cross the y-axis?

Where does the graph of y 2x 5 crosses the y-axis?

The y-value of the point where the line crosses the y-axis is called they-intercept. The equation y 2x 5 is written in slope-interceptform. The slope is 2, and the y-intercept is 5.

Slope-Intercept Form of a Linear Equationy mx b is a linear equation. The slope is m and they-intercept is b. The line crosses the y-axis at the point(0, b).



2y 3x 6 Given

122y

12(3x 6) Multiplication Property of Equality

y 32x 3 Distributive Property and Simplify

The slope is 32

, and the linecrosses the y-axis at (0, 3).

Now draw the coordinate axes. Graph the y-intercept (0, 3) as onepoint on the line. Since the slope is

23, you can find another point

by moving up 3 and to the left 2. Locate that point. Connect the twopoints with a line.

SOLUTION



4

3

2

1

The y-intercept see marginACTIVITY 2

y

x

(0, 3)

(2, 6)

y = – x + 332

. You can find another point by moving 3 units up and 2 units left. Locate that point. Connect the two points with a line.

y

x

(0, 3)

(�2, 6)

y = – x + 332

1–1

1

2

3

4

5

6

7

8

9

–1

–2

–3

–2–3–4–5–6 2 3 4 5 6



Critical Thinking How can you graph a line if you are given the slope and a point on the line? How is this similar to graphing an equation that is in slope-intercept form? Plot the point and then use the slope to plot another point. The y-interceptis also a point on the line.

Standard Form of an Equation

Another way to write linear equations is in standard form.

Standard Form of a Linear EquationAx By C, where A, B, and C are real numbers and A and B are not both zero.

Sometimes you may have to graph an equation that is in standard form. You can rewrite the equation in slope-intercept form. Then you can graph the equation using the slope and y-intercept.

Example 4 Writing Equations in Slope-Intercept Form

Write the equation 2x 4y 12 in slope-intercept form.

Solution

To write it in slope-intercept form, solve for y.



Standard Form of a Linear EquationAx By C, where A, B, and C are real numbers andA and B are not both zero.

Sometimes you may have to graph an equation that is in standardform. You can rewrite the equation in slope-intercept form. Thenyou can graph the equation using the slope and y-intercept.

Write the equation 2x 4y 12 is in standard form.


2x 4y 12

4y 2x 12 Subtraction Property of Equality

y 12

x 3 Division Property and Simplify

Therefore, the slope is 12

and the y-intercept is (0, 3).

Write the equation 3x y 2 in slope-intercept form. Graph the equation. y 3x 2; see margin for graph

Refer to the introductory paragraph about the baker's cookie recipe.Write an equation to model this situation. Then graph the equation.

• First, translate the problem into sentence form:

The number of cups of raisins plus the number of cups ofnuts plus

34

cup of chocolate chips must equal 3 cups.

• Second, let the letter r represent the number of cups of raisins andn represent the number of cups of nuts. Now you can change thesentence to the equation: r n

34

3.

SOLUTION


Ongoing Assessment

SOLUTION

EXAMPLE 4 Writing Equations in Slope-Intercept Form


Ongoing Assessment

Write the equation 3x y 2 in slope-intercept form. Graph the equation.y 3x 2; see margin for graph


Refer to the introductory paragraph about the baker's cookie recipe. Write an equation to model this situation. Then graph the equation.

Solution

l First, translate the problem into sentence form.

The number of cups of raisins plus the number of cups of nuts plus







2x 4y 12


y 12








34



34

3.

SOLUTION


Ongoing Assessment

SOLUTION



cup of dried fruit must equal 3 cups.


l Second, let r represent the number of cups of raisins and n represent the number of cups of nuts. Now you can change the sentence to the equation: r n







2x 4y 12


y 12








34



34

3.

SOLUTION


Ongoing Assessment

SOLUTION



To graph the equation, choose one of the variables as the independent variable. For example, let n be the independent variable. Then r takes the position of y, and n takes the position of x. To write the equation in slope-intercept form, isolate r on the left side of the equation.


To graph the equation, choose one of the variables as theindependent variable. For example, let n be the independentvariable. Then r takes the position of y, and n takes the position of x.To write the equation in slope-intercept form, isolate r on the leftside of the equation.

r n 34 3

r n n 34 3 n Subtraction Property of Equality

r 34

34 3 n

34 Subtraction Property of Equality

r n 214 Simplify.

By comparing the equation r n 214

with the slope-interceptform y mx b, you can see that the slope (m) is 1. So youwould expect this line to be higher on the left.

What numbers do you want to use on the r and naxes? Since the values for both will be smallpositive numbers, including fractions, you mightchoose a fairly large (1 inch or so) distance foryour unit. Draw the coordinate plans on yourpaper, mark the units, and label the axes.

You can use the y-intercept to locate one point anduse the slope to find another. Or you can make atable of several values. With only two orderedpairs, you can draw a straight line, but with severaladditional values, you can check your work. If allpoints are not on the same straight line, you havean error. If this happens, go back and check yourarithmetic—and the way you made the graph.Graph your values and draw the line.

The graph of the equation r n 214

is a linethat lies in quadrants one, two, and four. But thesituation in the problem makes sense only in thefirst quadrant, where both r and n are positivenumbers. As a result, the line you graph to fit theproblem is limited to the first quadrant. Use a solidline in the first quadrant to emphasize where thedata in the problem apply.

1

1

2

3

4

5r

0 2 3 4 5

n

1

1

2

4

5r

0 2 4 5

n

3

3

r = –n + 241

By comparing the equation r n



r n 34 3


r 34

34 3 n


r n 214 Simplify.







1

1

2

3

4

5r

0 2 3 4 5

n

1

1

2

4

5r

0 2 4 5

n

3

3

r = –n + 241

with the slope-intercept form y mx b, you can see that the slope (m) is 1. So you would expect this line to be higher on the left.

What numbers do you want to use on the r and n axes? Because the values for both will be small positive numbers, including fractions, make each unit



r n 34 3


r 34

34 3 n


r n 214 Simplify.







12

1

1

2

3

4

5r

0 2 3 4 5

n

1

1

2

4

5r

0 2 4 5

n

3

3

r = –n + 241

.

You can use the y-intercept to locate one point and use the slope to find another point. Or you can make a table of several values. With only two ordered pairs, you can draw a straight line, but with several additional values, you can check your work. If all points are not on the same straight line, you have an error. If this happens, go back and check your arithmetic—and the way you made the graph. Graph your values and draw the line.

The graph of the equation r n



r n 34 3


r 34

34 3 n


r n 214 Simplify.







1

1

2

3

4

5r

0 2 3 4 5

n

1

1

2

4

5r

0 2 4 5

n

3

3

r = –n + 241

is a line that lies in quadrants one, two, and four. But the situation in the problem makes sense only in the first quadrant, where both r and n are positive numbers. As a result, the line you graph to fit the problem is limited to the first quadrant. Use a solid line in the first quadrant to emphasize where the data in the problem apply.


Lesson AssessmentThink and Discuss

1. How can you use an equation to make a table?

2. How can you use a table to graph an equation?

3. Explain why m is the slope of the equation y mx.

4. Explain why the graph of the linear equation y mx b crosses the y-axis at (0, b).

Practice and Problem Solving

Identify the slope of the line represented by each equation. Find the y-intercepts.

5. y 5x 5; (0, 0) 6.


How can you use an equation to make a table?

How can you use a table to graph an equation?

Explain why m is the slope of the equation y mx.

Explain why the graph of the linear equation y mx bcrosses the y-axis at (0, b).

How can you graph the equation 3y x 9 using slope-intercept form?

Identify the slope of the line represented by eachequation? Find the x- and y-intercepts.

6. y 5x 5, (0, 0) 7. y 1203x

12

03, (0, 0) 8. y

23x 1

23,

32, 0,

9. y x + 1 1 10. y 35x 3

35 11. y 12 0

(1, 0), (0, 1) (5, 0), (0, 3) none, (0, 12)


5

4

3

2

1

Think and Discuss see margin

LESSON ASSESSMENT

CULTURAL CONNECTION see margin

Hypatia, the first womanmentioned in the history ofmathematics, wrote about thework of a mathematician knownas Diophantus of Alexandria.Sometime in the third centuryB.C.E., Diophantus wrote a textabout arithmetic. In his text,Diophantus worked withequations that have more thanone whole number solution. Theequations are called Diophantineequations. Consider thisproblem.

In a pet shop there are severalkittens and birds. The shopkeepercounted exactly 20 legs in the shop.How many kittens and birds doesthe shopkeeper have?

Let x represent the number of birdsand y the number of kittens. Thelinear equation 2x 4y 20models this situation.

There are an infinite number ofsolutions to the equation. But thesolution must make sense. Howmany kittens and birds can theshopkeeper have?

(0, 0)

7.








6. y 5x 5, (0, 0) 7. y 1203x

12

03, (0, 0) 8. y

23x 1

23,

32, 0,

9. y x + 1 1 10. y 35x 3

35 11. y 12 0

(1, 0), (0, 1) (5, 0), (0, 3) none, (0, 12)


5

4

3

2

1


LESSON ASSESSMENT






; (0, 1) 8. y x + 1 1; (0, 1)

9.








6. y 5x 5, (0, 0) 7. y 1203x

12

03, (0, 0) 8. y

23x 1

23,

32, 0,

9. y x + 1 1 10. y 35x 3

35 11. y 12 0

(1, 0), (0, 1) (5, 0), (0, 3) none, (0, 12)


5

4

3

2

1


LESSON ASSESSMENT






; (0, 3) 10. y 12 0; (0, 12)

Hypatia, the first woman mentioned in the history of mathematics, wrote about the work of a mathematician known as Diophantus of Alexandria. Sometime in the third century bce, Diophantus wrote a text about arithmetic. In his text, Diophantus worked with equations that have more than one whole number solution.

The equations are called Diophantine equations. Consider this problem.

A toy manufacturer uses the same type of wheel on a child’s bicycle as on a go-cart. Inventory records show only 20 of this type of wheel on hand. How many child bicycles and go-carts can be manufactured using the wheel inventory?

Let x represent the number of child bicycles and y represent the number of go-carts. The linear equation 2x 4y 20 models this situation.

There are an infinite number of solutions to the equation. But the solution must make sense. How many bicycles and go-carts can the toy manufacturer make?

Cultural ConneCtion see margin


Use the graphs and tables a–f to answer Exercises 11–13. a. b. x y

1 90 51 12 3

c. x y

1 40 41 42 4

d. e. f. x y

1 10 01 12 2

11. Is the slope of each line positive, negative, or neither?

12. What is the slope of each line?

13. What is the y-intercept of each line?

Graph each line given the slope and y-intercept. 14.

Use the graphs and tables a–f to answers Exercises 12–14. see margin

a. b. c.

d. e. f.



14. What is the y-intercept of each line?Graph each line given the slope and y-intercept. Identifythe zero of the graph. see margin

15. slope 12; y-int. 3 16. slope 3; y-int. 2


Graph each line given the slope and a point on the line.19. slope 2; (0, 3) 20. slope

35; (4, 3)

21. slope 13; (3, 1) 22. slope 4; (2, 6)

Graph each equation. Compare each graph to the parentfunction y x. see margin

23. y x 2 24. y 3x 5 25. y 2x 4

Graph each equation. Give the slope and y-intercept ofeach graph. see margin for graphs

26. x y 8 27. 2x y 6 28. 5x 2y 3

29. y 5x 3 30. 23

15x y 31. y x 4

32. An asphalt company has found the equation G 10 20L approximates the number of trucks of gravel required forsurfacing three-lane city streets. G represents the number oftrucks of gravel required and L represents the length of thestreet in kilometers.

a. What are the slope and y-intercept of the equation? 20; 10

m 1; b 8 m 2; b 6 m 52; b 2

3

m 5; b 3 m 15; b

23 m 1; b 4

x y1 9

0 51 12 3

x y1 4

0 41 42 4

x y1 1

0 01 12 2

15. slope 3; y-int. 2

16.


a. b. c.

d. e. f.







35; (4, 3)

21. slope 13; (3, 1) 22. slope 4; (2, 6)


23. y x 2 24. y 3x 5 25. y 2x 4


26. x y 8 27. 2x y 6 28. 5x 2y 3

29. y 5x 3 30. 23

15x y 31. y x 4



m 1; b 8 m 2; b 6 m 52; b 2

3

m 5; b 3 m 15; b

23 m 1; b 4

x y1 9

0 51 12 3

x y1 4

0 41 42 4

x y1 1

0 01 12 2

17. slope 0; y-int. 4

Graph each line given the slope and a point on the line. 18. slope 2; (0, 3) 19.


a. b. c.

d. e. f.







35; (4, 3)

21. slope 13; (3, 1) 22. slope 4; (2, 6)


23. y x 2 24. y 3x 5 25. y 2x 4


26. x y 8 27. 2x y 6 28. 5x 2y 3

29. y 5x 3 30. 23

15x y 31. y x 4



m 1; b 8 m 2; b 6 m 52; b 2

3

m 5; b 3 m 15; b

23 m 1; b 4

x y1 9

0 51 12 3

x y1 4

0 41 42 4

x y1 1

0 01 12 2

20.


a. b. c.

d. e. f.







35; (4, 3)

21. slope 13; (3, 1) 22. slope 4; (2, 6)


23. y x 2 24. y 3x 5 25. y 2x 4


26. x y 8 27. 2x y 6 28. 5x 2y 3

29. y 5x 3 30. 23

15x y 31. y x 4



m 1; b 8 m 2; b 6 m 52; b 2

3

m 5; b 3 m 15; b

23 m 1; b 4

x y1 9

0 51 12 3

x y1 4

0 41 42 4

x y1 1

0 01 12 2

21. slope 4; (2, 6)

Graph each equation. Compare each graph to the parent function y x.

22. y x 2 23. y 3x 5 24. y 2x 4

Graph each equation. Give the slope and y-intercept of each graph.

25. x y 8 26. 2x y 6 27. 5x 2y 3 . .


a. b. c.

d. e. f.







35; (4, 3)

21. slope 13; (3, 1) 22. slope 4; (2, 6)


23. y x 2 24. y 3x 5 25. y 2x 4


26. x y 8 27. 2x y 6 28. 5x 2y 3

29. y 5x 3 30. 23

15x y 31. y x 4



m 1; b 8 m 2; b 6 m 52; b 2

3

m 5; b 3 m 15; b

23 m 1; b 4

x y1 9

0 51 12 3

x y1 4

0 41 42 4

x y1 1

0 01 12 2

28. y 5x 3 29.


a. b. c.

d. e. f.







35; (4, 3)

21. slope 13; (3, 1) 22. slope 4; (2, 6)


23. y x 2 24. y 3x 5 25. y 2x 4


26. x y 8 27. 2x y 6 28. 5x 2y 3

29. y 5x 3 30. 23

15x y 31. y x 4



m 1; b 8 m 2; b 6 m 52; b 2

3

m 5; b 3 m 15; b

23 m 1; b 4

x y1 9

0 51 12 3

x y1 4

0 41 42 4

x y1 1

0 01 12 2

30. y x 4

.


a. b. c.

d. e. f.







35; (4, 3)

21. slope 13; (3, 1) 22. slope 4; (2, 6)


23. y x 2 24. y 3x 5 25. y 2x 4


26. x y 8 27. 2x y 6 28. 5x 2y 3

29. y 5x 3 30. 23

15x y 31. y x 4



m 1; b 8 m 2; b 6 m 52; b 2

3

m 5; b 3 m 15; b

23 m 1; b 4

x y1 9

0 51 12 3

x y1 4

0 41 42 4

x y1 1

0 01 12 2

.


31. An asphalt company has found the equation G 10 20L approximates the number of trucks of gravel required for surfacing three-lane city streets. G represents the number of trucks of gravel required and L represents the length of the street in kilometers.

a. What are the slope and G-intercept of the equation?

b. Complete a table for the street lengths and the number of trucks of gravel. Use street lengths between 1 and 10 kilometers.

c. Last week, the asphalt company used 130 truckloads of gravel. How much of the street did the company resurface?

32. You can tell roughly what the temperature (T ) is on a summer evening if you count how many times (N ) a cricket chirps in one minute. The formula to find the temperature in degrees fahrenheit is T


b. Complete a table for the street lengths and the number oftrucks of gravel. Use street lengths between 1 and 10kilometers. see margin

c. During one week, the asphalt company used 130 truckloads of gravel. How many kilometers of street didthe company resurface? 6

33. You can tell roughly what the temperature (T ) is on asummer evening if you count how many times (N ) a cricketchirps in one minute. The formula to find the temperature indegrees fahrenheit is T

14N 40.

a. Draw a graph of the formula. Use your graph to find thetemperature if you count 100 chirps per minute. Find howmany chirps you might hear if the temperature is 95 degrees.65°F; 220 chirps; see margin for graphb. What are reasonable values for T and N in this problem?Compare your graph to the one here. from 40°F to 110°F

34. In an experiment on plant growth, a certain species of plantis found to grow 0.05 centimeters per day. The plant measuredtwo centimeters when the experiment started. Let H representthe ending measurement of the plant. Let d represent thenumber of days during which the experiment takes place.

a. Make a table that models the growth of the plant. Write anequation from your table. H 0.05d 2

b. What are the slope and y-intercept for the equation? 0.05; 2

c. At the end of the experiment, the plant was 3.3 cm tall.How many days did the experiment last? 26 days

Write and solve an equation for each situation.35. Paul is going to use 30% of his savings to make a downpayment on a car. He can make a down payment of $2,500.How much does Paul have in his savings account? $8,333.33

36. Tamara charges $6 per hour to clean windows. She alsoreceives $3 for transportation to the job. One Saturday, Tamaraearned $39. How many hours did Tamara work? 6 hours

37. At 7 A.M., Jared notes that it is 15°C. The weatherforecaster reported that from 5 A.M. to 7 A.M., thetemperature rose 5°. What was the temperature at 5 A.M.?10°C

Mixed Review

1.0

cm.5

1.5

2.5

2.0

3.0

40. a. Draw a graph of the formula. Use your graph to find the

temperature if you count 100 chirps per minute. Find the number of chirps you might hear if the temperature is 95°F.

b. What are reasonable values for T and N in this problem?

33. In an experiment on plant growth, a certain species of plant is found to grow 0.05 centimeters per day. The plant measured two centimeters when the experiment started. Let H represent the ending measurement of the plant. Let d represent the number of days during which the experiment takes place.

a. Make a table that models the growth of the plant. Write an equation from your table.

b. What are the slope and y-intercept for the equation?

c. At the end of the experiment, the plant was 3.3 cm tall. How many days did the experiment last?

Mixed Review

34. Paul is going to use 30% of his savings to make a down payment on a car. He can make a down payment of $2,500. How much does Paul have in his savings account?

35. At 7 a.m., Jared notes that it is 15°C. The weather forecaster reported that from 5 a.m. to 7 a.m., the temperature rose 5°. What was the temperature at 5 a.m.?

1.0

cm.5

1.5

2.5

2.0

3.0

SW7216/Cord AlgebraFigure 5.48.A


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