1. 3.4 Find and Use Slopes of Lines

2. Basics of Slope
Slope (of a Line) – The vertical change (rise) of the line divided by the horizontal change (run) of the line.
Slope is represented by the letter m in an equation.
Rise
Run

3. Types of slopes Identify each type of slope in the graph above
Negative Slope
Driving Downhill
m is negative
Positive Slope
Driving Uphill
m is positive
Zero Slope
Driving on a flat road
m is 0
Undefined Slope
A cliff or a wall
m is undefined
Identify each type of slope in the graph above

4. Find the Slope when given two points
Remember slope is represented by m
m=rise/run
1. Label the x and y for each point
2. Rise –
The difference in vertical change
Subtract the y-values as shown
3. Run-
The difference in horizontal change
Subtract the x-values as shown
4. Divide the rise by the run
Rise
Run

5. Find the slope of the line
Remember slope is represented by m
Label your x and y for each point
Keep the slopes written as fractions
1. (0,4) and (4,0)
2. (0,4) and (5,8)
3. (-3, -2) and (4, 0)
4. (-2, 3) and (3, 3)
5. (2, -1) and (-1, 2)
Rise
Run

6. Comparing Slopes
The steeper line has the slope with the greater absolute value.

7. Parallel Slopes
Two lines are parallel if they have the same slope

8. Example: Find the slope of each line. Which lines are parallel?

9. Your Turn Find the slope of each line. Are the two lines parallel?

10. Perpendicular Slopes
Two lines are perpendicular if the product of their slopes is equal to -1.
The two slopes will be negative reciprocals
Negative reciprocal: Flip the fraction and change the sign

11. Example: Line h passes through (3, 0) and (7, 6)
Example: Line h passes through (3, 0) and (7, 6). Graph the line perpendicular to h that passes through the point (2, 5).

12. Your Turn
Find the slope of each line. Are the two lines perpendicular?
Line 1: (1, 1), (3, 3)
Line 2: (2, 2), (0,4)
Line 1: (-5, 2), (-3, 5)
Line 2: (-2, 2), (1, 0)
3. Line 1: (-2, 3), (-5, 2)
Line 2: (4, 1), (5, 3)

13. Graph a line given the slope and a point