Question

After x hours of rainfall today, Yvette recorded the amount of rain in inches, y, in a rain gauge. The table shows the

linear relationship for the recorded rainfall.

Rain Gauge

Time, x (hours)
3 4 5

Amount of Rain in Gauge, y (inches) 3.75 4.5 5.25


How many inches of rain was in the gauge before the rain began today, and what was the rate at which the rain fell
in inches per hour?

A. There was 0 inches in the rain gauge before the rain began, and the rain fell at a rate of 1.25 inches per hour.

B. There was 2.5 inches in the rain gauge before the rain began, and the rain fell at a rate of 1.25 inches per hour.

C. There was 3 inches in the rain gauge before the rain began, and the rain fell at a rate of 0.75 inch per hour.

D. There was 1.5 inches in the rain gauge before the rain began, and the rain fell at a rate of 0.75 inch per hour.

Answer 1

To find the answer, we need to determine the y-intercept and slope of the line that represents the linear relationship between time and the amount of rain.

Using the given data, we can calculate the slope as follows:

Slope = (change in y) / (change in x) = (5.25 - 3.75) / (5 - 3) = 1.25

Therefore, the rate at which the rain fell is 1.25 inches per hour.

To find the y-intercept, we can use one of the points on the line and the slope:

y = mx + b
3.75 = 1.25(3) + b
b = 0.25

Therefore, the amount of rain in the gauge before the rain began today was 0.25 inches.

The answer is A. There was 0 inches in the rain gauge before the rain began, and the rain fell at a rate of 1.25 inches per hour.