8-3 & 8-4: Graphing Linear Functions

Mr. Gallo

Graphing Linear Functions Linear Function:

The graph of this function is a ____________ _______. 

Graphs of the form y = mx

straight line

Graphing Linear Functions Example 1: Given the point A (3, 6), find the

equation of the line that passes through A and the origin.

What is the slope of the line?

______________________What could you multiply by 3 to get 6? _______________________The equation of the line is: y = x

6

3

6

32

2

2

Graphing Linear Functions Example 2-Given the point B (9, 3), find the

equation of the line that passes through B and the origin.

What is the slope of the line?

______________________ What could you multiply by 9 to get 3?

______________________ The equation of the line is:

y = x

3

9

1

3

1

3

1

3

3

9

The Slope Intercept Form The equation of line in the slope-intercept

form:

represents the _________.

represents the _______________. y-intercept is where the line crosses the y-axis

y bmx

m

b

slope

y -intercept

Example 3 - Graph the equation

What is the y-intercept?_______ What is the slope? ______

Example 4 - Graph the equation

What is the y-intercept?______ What is the slope? ______

0,52

1

0, 42

1

2 4y x

2 5y x

How are the graphs alike?

____________________

____________________

____________________

____________How are they different?

___________________

___________________

___________________

___________

2 4y x

2 5y x They have the

same slopes.

They have

different y –

intercepts.

Parallel lines

Example 5- Find the equation of the line with a y-intercept of 1 and a slope 3.

y bmx

Equation: _____________

m

b

slope

y intercept

3

1

3 1y x

Slope: _________.

Example 6- Find the equation of the line passing through (0, 6) and with slope −4.

4y x b

Equation: _____________

4

64y x

Substitute Point:

6 04 b

6 b

Example 7: Find the equation for the line passing through (3, −4) and (9, 0).

2

3y bx

Equation: _____________

36

2y x

Slope: _________.

Substitute Point:

2 1

2 1

y ym

x x

0 ( 4)

9 3

4

6

2

3

2

3

0 (2

39) b

0 6 b 6 b

Homework: 8.3-8.4 Worksheet