<u>Given:</u>
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)
<u>Slope</u>:
The slope can be determined using the formula,
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substituting the coordinates (0,12) and (3,10), we have;
![m=\frac{10-12}{3-0}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B10-12%7D%7B3-0%7D)
![m=\frac{-2}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-2%7D%7B3%7D)
Thus, the slope is ![m=-\frac{2}{3}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B2%7D%7B3%7D)