Question

For 19-21, use the following situation. You are filling up a pool in your backyard. After 4 minutes it is 2 feet deep

and after 10 minutes it is 5 feet deep.
19. Rate of change, m:
20. Initial value, b:
21. Linear equation that models this situation:

Answer 1

19. 1/2

20. 0

21. y = 1/2x + 0

Explanation:

The rate of change is 1/2 because to find the slope, or the rate of change, the equation is y/x, or rise over run.

Minutes, or time is the independent variable that is found along the x-axis of a graph, so we can substitute x for 4 minutes.

The amount of water in the pool changes over time, which correlates with the dependent variable, y. Thus, we can substitute 2 feet for y, giving us 2/4 or 1/2.

The initial value, b, is zero because the pool initially starts with no water in it.

The formula for a linear equation is y=mx+b, where m is the slope or rate of change and b is the y-intercept, the value of y at which it crosses the y-axis. Using the numbers from the previous answers, we can plug in our m and b values into the formula. After we plug in the values, you will get y = 1/2x + 0, or y = 1/2x. Hope this helps!