# Question: The grade of a road is defined as the distance

The grade of a road is defined as the distance it rises (or falls) to the distance it runs horizontally, usually expressed as a percentage. Consider a road with positive grade, g.

Suppose that you begin driving on that road at an altitude a0.

a. Find the linear equation that expresses the altitude, a, when you have driven a distance, d, along the road. (Hint: Draw a graph and apply the Pythagorean Theorem.)

b. Identify and interpret the y-intercept and slope of the linear equation in part (a).

c. Apply your results in parts (a) and (b) to a road with a 5% grade and an initial altitude of 1 mile. Express your answer for the slope to four decimal places.

d. For the road in part (c), what altitude will you reach after driving 10 miles along the road?

e. For the road in part (c), how far along the road must you drive to reach an altitude of 3 miles?

Suppose that you begin driving on that road at an altitude a0.

a. Find the linear equation that expresses the altitude, a, when you have driven a distance, d, along the road. (Hint: Draw a graph and apply the Pythagorean Theorem.)

b. Identify and interpret the y-intercept and slope of the linear equation in part (a).

c. Apply your results in parts (a) and (b) to a road with a 5% grade and an initial altitude of 1 mile. Express your answer for the slope to four decimal places.

d. For the road in part (c), what altitude will you reach after driving 10 miles along the road?

e. For the road in part (c), how far along the road must you drive to reach an altitude of 3 miles?

## Answer to relevant Questions

In this section, we stated that any nonvertical line can be described by an equation of the form y = b0 + b1x. a. Explain in detail why a vertical line can't be expressed in this form. b. What is the form of the equation of ...Line A: y = 3 − 0.6x Line B: y = 4 – x a. Graph the linear equations and data points. b. Construct tables for x, y, ˆy, e, and e 2 similar to Table 4.4 on page 151. c. Determine which line fits the set of data points ...The data points in Exercise 4.40 Line A: y = 1.5 + 0.5x Line B: y = 1.125 + 0.375x An instructor at Arizona State University asked a random sample of eight students to record their study times in a beginning calculus course. She then made a table for total hours studied (x) over 2 weeks and test score (y) ...How important are birdies (a score of one under par on a given golf hole) in determining the final total score of a woman golfer? From the U.S. Women's OpenWeb site, we obtained data on number of birdies during a tournament ...Post your question