Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain. The river was 22 feet before the rain began.(4 points)

Question

a. What is the rate of change (slope) for this scenario?
What is the y-intercept for this scenario?
c. Write an equation for the scenario in slope-intercept form
. Write this equation in standard form.

Answer 1

To find the rate of change (slope), we can use the formula:

slope = (change in y) / (change in x)

The change in y is the difference in water levels, which is 62 - 34 = 28 feet.
The change in x is the difference in days, which is 10 - 3 = 7 days.

So, the slope is: slope = 28 / 7 = 4 feet per day.

Since the river was 22 feet before the rain began, the y-intercept is 22.

Therefore, the equation for the scenario in slope-intercept form is:
y = 4x + 22

To write it in standard form, we need to rearrange the equation:
-4x + y = 22