Day 4

Slope of a Line

EMAT6690

by Chris Reid

The slope m of a nonvertical line is the number of units the line rises or falls for each unit of horizontal change from left to right.  Process for finding slope:

Given two points, label either point as (X1, Y1), and the other point as (X2, Y2). After labeling the points, you must subtract using the same order for the numerator and the denominator.

Correct: Incorrect: The order of the subtraction must match.

Example 1:

Find the slope of the line passing through the points (2, -2) and (4, 3).

Solution:

Let (X1, Y1) = (2, -2) and (X2, Y2) = (4, 3).    The slope of the line is 5/2.

A line with a zero slope is horizontal.

Example 2:

Find the slope of the line passing through the points (0, 4) and (-2, 4).

Solution:

Let (X1, Y1) = (0, 4) and (X2, Y2) = (-2, 4).    The graph of the line passing through the points (6, 4) and (-2, 4) is a horizontal line. A line with a zero slope is horizontal. The slope of a vertical line is undefined.

Example 3:

Find the slope of the line passing through the points (2, 4) and (2, 6).

Solution:

Let (X1, Y1) = (2, 4) and (X2, Y2) = (2, 6).    Since division by zero is undefined, 2/0 has no meaning.

The graph of the line passing through the points (2, 4) and (2, 6) is a vertical line. The slope of a vertical line in undefined. Assignment:

Find the slope of the line passing through each pair of points using the equation for slope.

1. (6, 9) and (0, -6)

2. (8, 0) and (4, 3)

3. (1, 5) and (-4, 0)

4. (0, -10) and (5, 2)

5. (1, -2) and (6, -2)

6. (2, -2) and (4, -3)

7. (8, -4) and (8, 6)

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

9. (-4, 6) and (-4, 7)

10. (0, 0) and (8, 7)