Question

a machine at a bakery is pouring out flour. the graph shows the amount of flour (in grams) in the machine versus time (in minutes). (a) what is the amount of flour in the machine at 0 minutes? grams (b) choose the statement that best describes how the time and amount of flour are related. then fill in the blank. as time increases, the amount of flour in the machine decreases. at what rate is the amount of flour decreasing? grams per minute as time increases, the amount of flour in the machine increases. at what rate is the amount of flour increasing? grams per minute

Explanation:

Step1: Solve part (a)

The graph's y - intercept (when \(x = 0\), time is 0 minutes) is at \(y=700\). So the amount of flour at 0 minutes is 700 grams.

Step2: Solve part (b) - Relationship

Looking at the graph, as time (x - value) increases, the amount of flour (y - value) decreases. So we choose "As time increases, the amount of flour in the machine decreases."

Step3: Solve part (b) - Rate of decrease

The slope of the line gives the rate of change. The line goes from \((0,700)\) to \((5,0)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 700}{5 - 0}=\frac{- 700}{5}=- 140\). The negative sign indicates a decrease, so the rate of decrease is 140 grams per minute.

Answer:

(a) 700
(b) The statement is "As time increases, the amount of flour in the machine decreases." and the rate is 140.