Section P.2 – Linear Models and Rates of Change

2 1

2 1

y yy

x x x

Slope Formula

The slope of the line through the points (x1, y1) and (x2, y2) is given by:

Forms of a Line

Point Slope Form - The equation of a line that contains the point (x1,y1) and whose slope is m is:

1 1y y m x x

Slope-Intercept Form - The equation of a line that contains the y-intercept (0,b) and whose slope is m is:

y mx b

General Form-

0Ax By C

Parallel and Perpendicular Lines

If the slope of line is then the slope

of a line…

• Parallel is

• Perpendicular is

am

b

am

b

bm

a

Example 1Algebraically find the slope-intercept equation of a

line that contains the points (-1,4) and (-4,-2).

2 1

2 1

y yx xm

2 44 1

63

2

4 2 1y x 4 2 2y x

1 1y y m x x 1 12y y x x 24 1y x

Find Slope

2 m

(-1,4)

(x1,y1)

(-4,-2)

(x2,y2)

2 6y x

Substitute into point-slope

Example 2Find an equation for the line that contains the point (2,-3) and is parallel to the

line .

2x y 6 0

Find the Slope of the original line:

2x y 6 0

Find the equation of the Parallel line:

Rewrite the equation into

Slope-Intercept

Form

m

Slope 2

y 2x 1

y 2x 6

y y1 m x x1 We know a

point and the slope

Parallel lines have same slope

y 2x 1

y 3 2 x 2

y 3 2x 4