1. 2.2 “Slope & Rate of Change”
Slope of a Line:
Slope:
m = 𝒚𝟐 − 𝒚𝟏 𝒙𝟐 − 𝒙𝟏
Rate of Change:
𝑽𝒆𝒓𝒕𝒊𝒄𝒂𝒍 𝑪𝒉𝒂𝒏𝒈𝒆 𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝑪𝒉𝒂𝒏𝒈𝒆 = 𝑹𝒊𝒔𝒆 𝑹𝒖𝒏

2. Examples
A skateboard ramp has a rise of 15 inches and a run of 54 inches. What is the slope?
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.

3. Classification of Lines By Slope
Positive Slope:
Negative Slope:
Zero Slope:
Undefined Slope:

4. Practice
Find the slope of the line that passes through the given points:
(3, 4) (6, -8)
(7, -4) (12, -4)
(1, 2) (-1, -8)
(-3, 7) (-3, -5)

5. Parallel & Perpendicular Lines
Parallel Lines: The slopes are the same.
Perpendicular Lines: The slopes are opposite reciprocals.

6. Example
Determine whether the lines are parallel, perpendicular or neither:
3y = x – 3
2y = – 6x – 12
Steps:
Put each equation into slope intercept form. y = mx + b
Determine whether parallel or perpendicular by looking at the m’s of both equations.
If you are given points instead of lines, find the slope of each.

7. Practice 10y = – 2x – 10 5y = – x (1, 2) (-1, -8) & (0, 3) (5,4)
(1, 2) (-1, -8) & (0, 3) (5,4)
4. (3, 4) (-3, 0) & (2, 1) (4, -2)

8. Word Problem

9. Finding Missing Values
1. Find the value of “k” so that the line through (k, 6) & (-7, 3) has a slope of 𝟑 𝟒
2. Find the value of “k” so that the line through (2k + 2, 1) & (k, 3) has a slope of −𝟐 𝟑