Answer:
A. -1.25 ft/hour — the number of feet the pool depth changes in 1 hour
B. 1 is the depth in feet of the pool when x=0 (at the start of it being filled)
Step-by-step explanation:
In these questions, the pool depth is represented by a linear equation in slope-intercept form. The equation gives depth in feet while the independent variable represents a number of hours.
A slope-intercept equation has the form
y = mx +b . . . where m is the slope (rate of change) and y is the intercept
The y-intercept (b) is the "initial value," the value of y when x=0.
__
A.
The equation ...
y = -1.25x +5
represents the depth of water in the Kim family pool. Comparing to the slope-intercept form, we see m = -1.25. That is, the "rate of change" is -1.25. When that value is multiplied by x hours, it gives a result in feet. That is, the units of the rate of change are feet/hour.
[tex]\dfrac{\text{feet}}{\text{hour}}\times\text{hours}=\text{feet}[/tex]
The "rate of change" of -1.25 in this context is telling you the depth is decreasing by 1.25 feet every hour as the pool is being drained.
__
B.
The equation ...
y = 1/2x +1
represents the depth of water in the Gutierrez family pool. Comparing to the slope-intercept form, we see b = 1. This is the initial value of depth, the value when x=0, the pool has been filling for 0 hours. It means the water in the pool is 1 foot deep when the pool starts filling.
