Q53. - Algebra 2

Question

53. WRITING IN MATH Answer the question that was posed at the beginning of the lesson.

How does slope apply to the steepness of roads?

Include the following in your answer:

• A few sentences explaining the relationship between the grade of a road and the slope of a line, and
• A graph of $\mathbf{y}=\mathbf{0}.\mathbf{08}\mathbf{x}$, which corresponds to a grade of 8% (A road with a grade of 6% to 8% is considered to be fairly steep. The scales on your $\mathbf{x}$- and $\mathbf{y}$-axes should be the same)

Step-by-Step Solution

Answer

• The grade of a road and the slope of a line are equivalent. Both of them measure the steepness.
• The graph of $y=0.08x$ is given as,
  
  

Step 1 – State the concept

The grade of a road is a percent that measures the steepness of the road. It is found by dividing the amount the road rises by the corresponding horizontal distance.

 

The slope of a line is the ratio of the change in y-coordinates to the corresponding change in x-coordinates.

 

Thus, in essence, if a road is treated as a straight line, then the grade of the road is nothing but the slope of the line representing the road.

Step 2 – List the given data

The given equation is $y=0.08x$ which corresponds to a grade of 8%.

Step 3 – Construct the graph

The graph of the given equation, $y=0.08x$ is given as follows: