Question

the table shows the height of water in a pool as it is being filled.

time (min)	height (in.)
4	12
6	16
8	20
10	24

the slope of the line through the points is 2. which statement describes how the slope relates to the height of the water in the pool?

• the height of the water was 2 inches before any water was added.
• the height of the water decreases 2 inches per minute.
• the height of the water increases 2 inches per minute.
• the height of the water will be 2 inches when the pool is filled.

Explanation:

The slope of a line in a context like this (relating time and height of water) represents the rate of change. The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \(x\) is time (in minutes) and \(y\) is height (in inches). A positive slope means the height is increasing over time. Here, the slope is 2, so for each unit increase in \(x\) (each minute), \(y\) (height) increases by 2. So we analyze each option:

• "The height of the water was 2 inches before any water was added." This refers to the y - intercept (when \(x = 0\)), not the slope.
• "The height of the water decreases 2 inches per minute." A negative slope would mean a decrease, but our slope is positive, so this is wrong.
• "The height of the water increases 2 inches per minute." This matches the interpretation of a positive slope of 2 (rate of change of height with respect to time).
• "The height of the water will be 2 inches when the pool is filled." The slope doesn't tell us the final height, it tells us the rate of change.

Answer:

The height of the water increases 2 inches per minute.