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,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the coordinates (0,12) and (3,10), we have;
[tex]m=\frac{10-12}{3-0}[/tex]
[tex]m=\frac{-2}{3}[/tex]
Thus, the slope is [tex]m=-\frac{2}{3}[/tex]
