## Solving Slope Applications

At the beginning of this section, we said there are many applications of slope in the real world. Let’s look at a few now.

## Example

The pitch of a building’s roof is the slope of the roof. Knowing the pitch is important in climates where there is heavy snowfall. If the roof is too flat, the weight of the snow may cause it to collapse. What is the slope of the roof shown?

### Solution

Use the slope formula. | \(m=\frac{\text{rise}}{\text{run}}\) |

Substitute the values for rise and run. | \(m=\frac{\text{9 ft}}{\text{18 ft}}\) |

Simplify. | \(m=\frac{1}{2}\) |

The slope of the roof is \(\frac{1}{2}\). |

Have you ever thought about the sewage pipes going from your house to the street? Their slope is an important factor in how they take waste away from your house.

## Example

Sewage pipes must slope down \(\frac{1}{4}\) inch per foot in order to drain properly. What is the required slope?

### Solution

Use the slope formula. | \(m=\frac{\text{rise}}{\text{run}}\) |

\(m=\frac{-\frac{1}{4}\phantom{\rule{0.2em}{0ex}}\text{in}\text{.}}{1\phantom{\rule{0.2em}{0ex}}\text{ft}}\) | |

\(m=\frac{-\frac{1}{4}\phantom{\rule{0.2em}{0ex}}\text{in}\text{.}}{1\phantom{\rule{0.2em}{0ex}}\text{ft}}\) | |

Convert 1 foot to 12 inches. | \(m=\frac{-\frac{1}{4}\phantom{\rule{0.2em}{0ex}}\text{in}\text{.}}{12\phantom{\rule{0.2em}{0ex}}\text{in.}}\) |

Simplify. | \(m=-\frac{1}{48}\) |

The slope of the pipe is \(-\frac{1}{48}.\) |