EDGE Math 8

Slope of a Line

Example

Find the slope of the line with equation $y = 6.$

Solution

Take any two distinct points on the line. Then compute its slope using these points. Recall that any point on the line with equation $y = 6$ has coordinates of the form $(k, 6) .$ For instance, you may take the points $(10, 6)$ and $(3, 6) .$ Using these two points, the slope of the line can be computed as follows:

m = \frac{6 - 6}{3 - 10} = \frac{0}{- 7} = 0.

Note that the graph of the equation $y = 6$ in the preceding example is a horizontal line and that its slope is equal to 0. In general, all lines with a slope of 0 are horizontal.

Notice also that in the definition of the slope of the line that passes through the points $P (x_{1}, y_{1})$ and $Q (x_{2}, y_{2}),$ the formula for the slope given by

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}},

provided that

x_{2} \neq x_{1} .

If $x_{2} = x_{1},$ then points P and Q will have the same x-coordinate, and the slope of the line will be undefined. It also follows that the line containing points P and Q is vertical. In general, the slope of any vertical line is undefined.