Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. The river was 60 feet before the drought began.

Question

a. What is the rate of change (slope) for this scenario? ________________
b. What is the y-intercept for this scenario? ________________
c. Write an equation for the scenario in slope-intercept form ______________
d. Write an equation in standard form ____________
Options: (-5, 0), y = 5x + 45, 5x + y = 60, (0, -5), 15, y = -5x + 60, 5, (0, 60), y = -5x - 35, -5, 5x + y = 35, -5x + y = 60

Answer 1

To find the values for the river's water level in relation to the number of days without rain, we can study the data given.

a. Rate of change (slope)

The water level decreases from 60 feet to 45 feet after 3 days and then to 10 feet after 10 days.

1. From 3 days to 10 days:
   Water level decreases from 45 feet to 10 feet.
   Change in water level = \(10 - 45 = -35\) feet
   Change in time = \(10 - 3 = 7\) days
   Slope = \(\frac{-35 \text{ feet}}{7 \text{ days}} = -5 \text{ feet per day}\)

Thus, the rate of change (slope) is -5.

b. y-intercept

To find the y-intercept, we know the river was 60 feet before the drought began (when \(x = 0\)).

Thus, the y-intercept is (0, 60).

c. Equation in slope-intercept form

Using the slope \(m = -5\) and the y-intercept \(b = 60\), we can write the slope-intercept form of the equation:

\(y = -5x + 60\).

d. Equation in standard form

To convert the slope-intercept form \(y = -5x + 60\) into standard form \(Ax + By = C\), we rearrange it:

\[ 5x + y = 60. \]

Thus, the answers are:

a. -5
b. (0, 60)
c. \(y = -5x + 60\)
d. \(5x + y = 60\)