1. 2.2 Slope and Rate of Change
Algebra 2

2. Learning Targets
I can find slopes of lines and classify parallel and perpendicular lines.
I can use slope to solve real-life problems.

3. The slope of a nonvertical line is the ratio of vertical change (the rise) to the horizontal change (the run).
The slope of a line is represented by the letter m.
Just like any 2 points determine a line, any 2 points are all that are needed to determine the slope.
The slope of the line is the same regardless of which 2 points are used

4. The slope of a line
The slope of a nonvertical line passing thru the points (x1,y1) (x2,y2):

5. Find the slope of a line passing thru (-3,5) & (2,1)

6. Classification of lines by slope
A line with positive slope: rises from left to right (m>0)
A line with negative slope: falls from left to right (m<0)
A line with slope of zero is horizontal (m=0)
A line with undefined slope is vertical (m is undefined)

7. W/out graphing, tell whether the line thru the points rises, falls, horizontal, or vertical.
1) (3,-4), (1,-6)
2) (2,-1), (2,5)
m>0, the line rises
Undefined:
The line is
vertical

8. Not only does slope tell you whether the line rises, falls, is horizontal, or is vertical; it also tells you the steepness of the line
For two lines, the line slope of greater absolute value is steeper.

9. Tell which line is steeper
Line 1 thru (2,3) & (4,7)
or Line 2 thru (-1,2) & (4,5)
Since the lines have positive slope &
m1>m2 line 1 is steeper

10. Parallel and Perpendicular Lines
Two lines are parallel if they don’t intersect.
Two lines are perpendicular if they intersect to form a right angle.

11. Slope can be used to determine if 2 lines are װ or ┴
Parallel Lines
װ lines m1 = m2 (the slopes are =)
Perpendicular Lines
┴ lines (negative reciprocals)

12. Tell whether the lines are װ,┴, or neither
L1: thru (-3,3) & (3,-1)
L2: thru (-2,-3) & (2,3)
Negative reciprocals
Of each other :
They are ┴.

13. Using slope. Turn to p. 78 ladder problem.
Max recommended slope m=12/3=4
X=min distance from wall to reach 20’
Write a proportion
The rise is 20, the run is X
Cross multiply and solve
X=5 The ladder’s base should be 5’ from the wall 12 3 20 X

14. Pair-share
Work on 2.2 Practice B classwork.

15. Homework
pp #4-47 all

16. Resources: Modified from the website below: