Question

1. a driveway rises 1.5 m from the street level to the carport, which is a horizontal distance of 6 m from the street

a) how long is the driveway?

b) what is the slope of the driveway?

Explanation:

Step1: Identify right - triangle sides

The vertical rise is $a = 1.5$ m and the horizontal distance is $b = 6$ m. The driveway length $c$ is the hypotenuse of a right - triangle.

Step2: Apply Pythagorean theorem

By the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 1.5$ and $b = 6$ into the formula: $c=\sqrt{(1.5)^{2}+6^{2}}=\sqrt{2.25 + 36}=\sqrt{38.25}\approx6.18$ m.

Step3: Recall slope formula

The slope $m$ of a line is given by the ratio of the vertical change to the horizontal change. For the driveway, $m=\frac{\text{vertical change}}{\text{horizontal change}}$.

Step4: Calculate the slope

Substitute the vertical rise of $1.5$ m and horizontal distance of $6$ m into the slope formula. $m=\frac{1.5}{6}=\frac{1}{4}=0.25$.

Answer:

a) The length of the driveway is approximately $6.18$ m.
b) The slope of the driveway is $0.25$.