Question

this scatter - plot shows the association between time elapsed and distance left to go when john drove from city a to city b. what are the slope and the y - intercept of the line of best fit on the scatter - plot?
distance (miles)
120
100
80
60
40
20
0
20 40 60 80 100 120
time (minutes)
a. the y - intercept is 80, and the slope is 0.
b. the y - intercept is 80, and the slope is -\frac{2}{3}.
c. the y - intercept is 0, and the slope is +\frac{2}{3}.
d. the y - intercept is 15, and the slope is \frac{2}{3}.
e. the y - intercept is 0, and the slope is \frac{1}{3}.

Explanation:

Step1: Identify y - intercept

The y - intercept is the value of y when x = 0. Looking at the scatter - plot, when time (x) = 0 minutes, the distance (y) is 80 miles. So the y - intercept is 80.

Step2: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Choose two points on the line of best - fit, say (0, 80) and (120, 0). Then $m=\frac{0 - 80}{120-0}=\frac{-80}{120}=-\frac{2}{3}$.

Answer:

B. The y - intercept is 80, and the slope is $-\frac{2}{3}$