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Question

Solve each problem by graphing. A builder constructs a skateboard ramp with a slope of $\frac{1}{8}$. Find the length of a ramp that increases 5 ft in height.

Solution

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The slope of the ramp is $\frac{1}{8}$.

Let $x$ represent the length of the ramp and let $y$ represent the height of the ramp.

We let the bottom edge of the skateboard ramp be at the origin of the graph and thus (0,0) is a point on the ramp.

The slope represents the average increase in the $y$-value per unit of $x$ and thus $y$ is on average $\frac{1}{8}$ when $x=1$ (as $(0,0)$ is a point on the ramp), thus $\left(1,\frac{1}{8}\right)$ is also a point on the ramp.

We can then graph the situation by graphing $(0,0)$ and $\left(1,\frac{1}{8}\right)$, and then drawing a straight line through the two points (which will contain the ramp).

Next, we sketch a horizontal line that intersects the vertical axis at 5, then we draw a vertical line through the intersection of the horizontal line and the sketched straight line. We then note that this vertical line intersects the horizontal axis at about 40 and thus the length of the ramp is about 40 feet.

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