“Friendship is born at that moment when one person says to another, ‘What! You too? I thought I was the only one.’”

-C. S. Lewis

Ch. 2 Notes Page 7P7 2.2: Linear Equations Part 1

“Failure is not falling down, but refusing to get back up.” – Chinese Proverb

Linear Functions/Equations

Graphing Linear Equations

y = mx + b• y is called the dependent variable because the value of y depends on x

• x is called the independent (or control) variable

Example: Using a table, graph the equation:

33

2 xy

x y (x, y)33

2 xy

Standard Form

Standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers and A, B ≠ 0.

You can graph linear equations in standard form by finding the x- and y- intercepts

Example: Graph x + y = -2

More Practice

The equation 3x + 2y = 120 models the number of passengers who can sit in a train car. X is the number of adults and y is the number of children.

What are the x- and y- intercepts?

What do they represent?

What is the domain? Range?

Slope

)(

)(

runx

riseyslope

Example: What is the slope of the line through the points (-3, 4) and (8, -1)?

Example: What is the slope of the line through the points (-2,-2) and (4,2)?

Slope (cont.)

)(

)(

runx

riseyslope

What does it mean if the slope is zero? Undefined?

“Friendship is born at that moment when one person says to another, ‘What! You too? I thought I was the only one.’”

-C. S. Lewis

“Failure is not falling down, but refusing to get back up.” – Chinese Proverb

2.2: Linear Equations Part 1HW #4: 2-2 P67 #3, 6, 8, 11-13, 17-19

“Friendship is born at that moment when one person says to another, ‘What! You too? I thought I was the only one.’”

-C. S. Lewis

Ch. 2 Notes Page 8P8 2.2: Linear Equations Part 2

“Failure is not falling down, but refusing to get back up.” – Chinese Proverb

Types of Equations

Slope-Intercept Form y=mx+b

Standard Form Ax+By=C

Point-Slope Form y-y1=m(x-x1)

Horizontal Lines & Vertical Linesy=Number x=Number

Parallel and Perpendicular LinesSlopes and Reciprocals

Slope-Intercept Form

y = mx + b

m=3 and (2,4)

Standard Form

Ax+By=C

4x+8y=24 Find the x- and y-intercepts

Point-Slope Form

The line through the point (x1, y1) with slope m has the equation

y – y1 = m(x – x1)

Example: Find the equation of a line with slope through the point (-6, 2). Write it in standard form. 3

1

Point-Slope Form

The line through the point (x1, y1) with slope m has the equation

y – y1 = m(x – x1)

Example: Find the equation of a line through the points (-2, 3) and (1, 6). Write it in standard form.

Slope-Intercept Form

y = mx + b

What is the slope of the line 4x + 6y = 18?

What is the slope of:

a horizontal line?

a vertical line?

parallel lines?

perpendicular lines?

Example: Write an equation through the point (3, 5) and perpendicular to the line 7x – 21y = 42

3 equations for a line

Slope-intercept: y = mx + b

slope y-intercept

Point-slope: y – y1 = m ( x – x1 )

(x,y) point on line

Standard Form: A x + B y = C

numbers

“Friendship is born at that moment when one person says to another, ‘What! You too? I thought I was the only one.’”

-C. S. Lewis

“Failure is not falling down, but refusing to get back up.” – Chinese Proverb

2.2: Linear Equations Part 2HW #5: 2-2 P68 #20, 24, 26, 30, 32, 36, 43,

45, 48, 51, 57