Teaching Notes 4.8: Using Equations to Find the Slopes of
Lines
The concept of slope is difficult for many students to master. Especially confusing are the slopes
of horizontal and vertical lines. Students often confuse a slope of 0 with no slope as well as which
type of line has no slope and which lines have a slope of 0.- Explain the formula that is used to find the slope of a line:m=
y 2 −y 1
x 2 −x 1. Ask your students
to find the slope of a line through points (3, 4) and (6, 8). In this case, the slope is 2.
2. Draw a horizontal line; for example,y=4. Ask your students to select two points on the line.
The coordinates of the points may vary but they-values are the same. As students apply the
slope formula, they will note that the numerator is equal to 0. This is true for all horizontal
lines. Therefore the slope of a horizontal line is 0.
3. Draw a vertical line; for example,x=3. Ask your students to select two points on the line.
The coordinates of the points may vary but thex-values are the same. As students apply the
slope formula, the denominator is equal to 0. This is true for all vertical lines. Emphasize that
because division by 0 is undefined, a vertical line has no slope.
4. Review the information on the worksheet with your students. Note that some equations may
have to be rewritten so that they are expressed in slope-intercept form.
EXTRA HELP:
Think of a horizontal line as flat, not steep. The slope of the line is 0.ANSWER KEY:
(1)m= 2 (2)No slope (3)m= 0 (4)m= 0(5)m=− 1 (6)No slope (7)m=− 2 (8)m= 1
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(Challenge)Answers may vary. Any equation of the formy=mx+6 is correct, provided that the
slope is not equal to 0.
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