Question

1. (3 pts) the table below shows the hours, x, spent working on a new road and the distance, y, of the finished road.

time (hours)	distance(miles)
200	6
350	10.5
400	12
650	19.5

part a. what is the slope of the line that fits these data?
a. $\frac{3}{400}$
b. $\frac{3}{100}$
c. $\frac{3}{25}$
d. 3
part b. what is the meaning of the slope?
part c. what is the meaning of the y - intercept?

Explanation:

Step1: Recall slope formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can take any two - points from the table. Let's take $(x_1,y_1)=(50,1.5)$ and $(x_2,y_2)=(200,6)$.

Step2: Calculate the slope

$m=\frac{6 - 1.5}{200 - 50}=\frac{4.5}{150}=\frac{45}{1500}=\frac{3}{100}$.

Step3: Interpret the slope

The slope represents the rate of change. In this context, it means that for every 1 hour of work, $\frac{3}{100}$ miles of the road is completed.

Step4: Consider the y - intercept

Since when $x = 0$ (no work has been done), $y=0$ (no road is completed), the y - intercept is 0. It means that without any time spent working on the road, the distance of the finished road is 0 miles.

Answer:

Part A: B. $\frac{3}{100}$
Part B: The rate at which the road is being completed is $\frac{3}{100}$ miles per hour.
Part C: When no time is spent working on the road, the distance of the finished road is 0 miles.