Question

a machine at a bakery is pouring out flour. the graph shows the amount of flour (in grams) versus time (in minutes).
(a) what is the amount of flour in the machine at 0 minutes?
630 grams
(b) choose the statement that best describes how the time and amount of flour are related.
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: Analyze the graph for part (a)

From the graph, at \( x = 0 \) (0 minutes), the \( y \)-value (amount of flour) is 630 grams. So the amount of flour at 0 minutes is 630 grams.

Step2: Analyze the relationship for part (b)

The graph is a line with a negative slope (going down from left to right), so as time (x - value) increases, the amount of flour (y - value) decreases. To find the rate of decrease, we use the two points: at \( x = 0 \), \( y = 630 \); at \( x = 3 \), \( y = 0 \). The rate of change (slope) is \( \frac{\Delta y}{\Delta x}=\frac{0 - 630}{3 - 0}=\frac{- 630}{3}=- 210 \) grams per minute. The negative sign indicates a decrease, so the rate of decrease is 210 grams per minute. For the increasing case, since the slope is negative, the amount is not increasing, but if we consider the other option (though incorrect for this graph), but based on the graph, the correct relationship is decrease.

Answer:

(a) 630 grams
(b) Statement: "As time increases, the amount of flour in the machine decreases."
Rate of decrease: 210 grams per minute
(For the increasing rate, since the graph shows a decrease, there is no increasing rate here. If we assume a mis - reading, but based on the graph, the decrease rate is 210 grams per minute)