2.2 “Slope & Rate of Change”Slope:

m =

Rate of Change:

=

Slope of a Line:

Examples1. A skateboard ramp has a

rise of 15 inches and a run of 54 inches. What is the slope?

2. What is the slope of the line passing through the points (-2, 1) and (3, 5)?

***Label the points, reduce if possible, and leave as a fraction.

Classification of Lines By SlopePositive Slope:

Negative Slope:

Zero Slope:

Undefined Slope:

PracticeFind the slope of the line that passes through the given points:

1. (3, 4) (6, -8)

2. (7, -4) (12, -4)

3. (1, 2) (-1, -8)

4. (-3, 7) (-3, -5)

Parallel & Perpendicular LinesParallel Lines: The slopes are the same.

Perpendicular Lines: The slopes are opposite reciprocals.

ExampleDetermine whether the lines are parallel, perpendicular or neither:

1. 3y = x – 3 2y = – 6x – 12

Steps:

1. Put each equation into slope intercept form. y = mx + b

2. Determine whether parallel or perpendicular by looking at the m’s of both equations.

3. If you are given points instead of lines, find the slope of each.

Practice2. 10y = – 2x – 10 5y = – x

3. (1, 2) (-1, -8) & (0, 3) (5,4)

4. (3, 4) (-3, 0) & (2, 1) (4, -2)

Word Problem

Finding Missing Values1. Find the value of “k” so that the line through (k, 6) & (-7, 3) has a slope of

2. Find the value of “k” so that the line through (2k + 2, 1) & (k, 3) has a slope of