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Graph the line with the given intercept and slope: $\left(\mathrm{-2},1\right),m=3.$
Graph the line with the given intercept and slope: $\left(4,\mathrm{-2}\right),m=\mathrm{-2}.$
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.
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?
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 $\frac{1}{2}$ . |
Find the slope given rise and run: A roof with a rise $=14$ and run $=24.$
$\frac{7}{12}$
Find the slope given rise and run: A roof with a rise $=15$ and run $=36.$
$\frac{5}{12}$
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.
Sewage pipes must slope down $\frac{1}{4}$ inch per foot in order to drain properly. What is the required slope?
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 $-\frac{1}{48}.$ |
Find the slope of the pipe: The pipe slopes down $\frac{1}{3}$ inch per foot.
$-\frac{1}{36}$
Find the slope of the pipe: The pipe slopes down $\frac{3}{4}$ inch per yard.
$-\frac{1}{48}$
Use Geoboards to Model Slope
In the following exercises, find the slope modeled on each geoboard.
In the following exercises, model each slope. Draw a picture to show your results.
$\frac{3}{4}$
$\frac{4}{3}$
$-\frac{3}{4}$
$-\frac{3}{2}$
Find the Slope of a Line from its Graph
In the following exercises, find the slope of each line shown.
Find the Slope of Horizontal and Vertical Lines
In the following exercises, find the slope of each line.
$y=\mathrm{-3}$
$x=\mathrm{-4}$
Use the Slope Formula to find the Slope of a Line between Two Points
In the following exercises, use the slope formula to find the slope of the line between each pair of points.
$\left(2,3\right),\left(5,7\right)$
$\left(0,1\right),\left(5,4\right)$
$\left(3,6\right),\left(8,0\right)$
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