Question

use the following information to answer the next question.

1. what is the slope of the above line?

a. -\frac{5}{9}
b. -\frac{9}{5}
c. \frac{5}{9}
d. \frac{9}{5}
numerical response

1. what is the slope of a 112% grade? write your answer as a decimal to two places. (record your answer in the numerical - response section on the answer sheet.)
2. a ramp is 26 inches high and has a run of 16 feet. how long is the ramp diagonally? round to the nearest inch. (hint: convert feet to inches) (record your answer in the numerical - response section on the answer sheet.)

Explanation:

Step1: Recall slope - formula for question 6

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Assume two points on the line: if we assume the $y$-intercept is at $(0,5)$ and another point is at $(9,0)$. Then $m=\frac{0 - 5}{9-0}=-\frac{5}{9}$.

Step2: Understand grade as slope for question 7

A grade of $n\%$ is equivalent to a slope $m=\frac{n}{100}$. For a $112\%$ grade, $m = \frac{112}{100}=1.12$.

Step3: Use Pythagorean theorem for question 8

First, convert the run from feet to inches. Since 1 foot = 12 inches, a run of 16 feet is $16\times12 = 192$ inches. The height of the ramp is $a = 26$ inches and the run is $b=192$ inches. By the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}=\sqrt{26^{2}+192^{2}}=\sqrt{676 + 36864}=\sqrt{37540}\approx202$ inches.

Answer:

1. A. $-\frac{5}{9}$
2. 1.12
3. 202 inches