Question

148. Draw the segment from (3, 1) to (5, 6), and the segment from (0, 5) to (2, 0). Calculate their slopes. You should notice that the segments are equally steep, and yet they differ in a significant way. Do your slope calculations reflect this difference?

Answer 1

First, we draw the segments:

Now, to compute the slopes of the segments we use the following formula:

$s=\frac{y_2-y_1}{x_2-x_1}\text{.}$

The slope of the red segments is:

$s_r=\frac{6-1}{5-3}=\frac{5}{2}\text{.}$

The slope of the blue segments is:

$s_b=\frac{0-5}{2-0}=\frac{-5}{2}=-\frac{5}{2}\text{.}$

Notice that the absolute value of the slopes is the same but the values are the negative of each other, so the segments are equally steep but in opposite directions.