Question

Take west to be the positive direction. The height of a sloped roof above the place where you stand is 12

Answer 1

Given:

Take west to be the positive direction. The height of a sloped roof above the place where you stand is 12  feet. If you move 3 feet west, the height is 10 feet.

We need to determine the slope.

Let x denote the standing place.

Let y denote the height.

Writing the given as coordinates, we get;

(0,12) and (3,10)

Slope:

The slope can be determined using the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the coordinates (0,12) and (3,10), we have;

$m=\frac{10-12}{3-0}$

$m=\frac{-2}{3}$

Thus, the slope is $m=-\frac{2}{3}$