Question

A local road has a grade of 5%. The grade of a road is its slope expressed as a percent. What is the slope? What is the rise? What is the run?

Answer 1

`\begin{gathered} a)\text{ }(1)/(20) \\ b)\text{ Rise:1 ft, Run: 20ft} \end{gathered}`

a) Since the grade is given by the slope, and the grade has a 5%.

We can rewrite it as a fraction, like this:

`(5)/(100)=(1)/(20)`

Note that we have simplified this to 1/20 by dividing the numerator and the denominator (bottom number) by 5

So, the slope is:

`(1)/(20)`

b) The "rise" is the difference between two coordinates on the y-axis and the "run" is the subtraction between two coordinates on the x-axis. Let's remember the slope formula and the Cartesian plane:

`m=(y_2-y_1)/(x_2-x_1)=(1)/(20)`

So the "rise" for this grade is 1 foot and the run is 20 feet.

3) Hence, the answers are:

`\begin{gathered} a)\text{ }(1)/(20) \\ b)\text{ }Rise\colon\text{ }1\text{ Run: 20} \end{gathered}`