1. 3.4 Find and Use Slopes of Lines
Define the following words:
Slope
Rise
Run
- The rate of change
- The change in y
- The change in x

2. Key Concept: Slope of lines in the Coordinate Plane
Negative slope: falls from left to right
Positive slope: rises from left to right
Zero slope – horizontal
Undefined slope: vertical

3. EXAMPLE 1
Find slopes of lines in a coordinate plane
Find the slope of line a and line d.
SOLUTION
y2 – y1
x2 – x1 = =
4 – 2
6 – 8 = 2
– 2
Slope of line a: m =
– 1
y2 – y1
x2 – x1 = =
4 – 0
6 – 6 = 4
Slope of line d: m
which is undefined.

4. Postulate 17: Slopes of Parallel Lines
In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope.
m || n

5. EXAMPLE 2
Identify parallel lines
Find the slope of each line. Which lines are parallel?
SOLUTION
Find the slope of k1 through (– 2, 4) and (– 3, 0). m1 =
0 – 4
– 3 – (– 2 ) =
– 4
– 1 = 4
Find the slope of k2 through (4, 5) and (1, 3). m2
1 – 5
3 – 4 = =
– 4
– 1 = 4

6. EXAMPLE 2
Identify parallel lines
Find the slope of k3 through (6, 3) and (5, – 2). m3
– 2 – 3
5 – 6 = =
– 5
– 1 5
Compare the slopes. Because k1 and k2 have the same slope, they are parallel. The slope of k3 is different, so k3 is not parallel to the other lines.

7. Postulate 18: Slopes of Perpendicular Lines
In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1.

8. EXAMPLE 3
Draw a perpendicular line
Line h passes through (3, 0) and (7, 6). Graph the line perpendicular to h that passes through the point (2, 5).
SOLUTION
STEP 1
Find the slope m1 of line h through (3, 0) and (7, 6). m1 =
6 – 0
7 – 3 = 6 4 = 3 2

9. Draw a perpendicular line
EXAMPLE 3
Draw a perpendicular line
STEP 2
Find the slope m2 of a line perpendicular to h. Use the fact that the product of the slopes of two perpendicular lines is –1. m2 = 3 2
– 1
Slopes of perpendicular lines m2 =
– 2 3 2 3
Multiply each side by
STEP 3
Use the rise and run to graph the line.

10. EXAMPLE 4
Standardized Test Practice
SOLUTION
The rate at which the skydiver descended is represented by the slope of the segments. The segments that have the same slope are a and c.
The correct answer is D.
ANSWER