Question

1. the graph shows the volume of water in a sink x minutes after the faucet is turned on. water in sink part a what is the slope of the line? part b connor says the graph shows that water is flowing at a rate of 2 gallons per minute. is he correct? explain.

Explanation:

Step1: Select two points on the line

We can choose (0,0) and (8,4) from the graph.

Step2: Apply slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(8,4)$ gives $m=\frac{4 - 0}{8 - 0}=\frac{4}{8}=\frac{1}{2}$.

Step3: Analyze Connor's statement

The slope represents the rate of change. Here, the slope $\frac{1}{2}$ means the volume of water increases by $\frac{1}{2}$ gallon per minute. So Connor is incorrect.

Answer:

Part A: $\frac{1}{2}$
Part B: No. The slope of the line is $\frac{1}{2}$, which means water is flowing at a rate of $\frac{1}{2}$ gallon per minute, not 2 gallons per minute.