Question

iris picked a bucket of raspberries to make jam. the table shows the cups of raspberries left in the bucket, y, as a function of the number of batches of jam she makes, x. is the rate of change positive or negative? positive negative batches, x raspberries left in bucket (cups), y 1 16 4 10 7 4

Explanation:

Step1: Recall Rate of Change Formula

The rate of change (slope) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Calculate Rate Between (1,16) and (4,10)

Using \(x_1 = 1,y_1 = 16,x_2 = 4,y_2 = 10\), the rate is \(\frac{10 - 16}{4 - 1}=\frac{-6}{3}=- 2\).

Step3: Calculate Rate Between (4,10) and (7,4)

Using \(x_1 = 4,y_1 = 10,x_2 = 7,y_2 = 4\), the rate is \(\frac{4 - 10}{7 - 4}=\frac{-6}{3}=-2\).
Since the rate of change is negative (both calculations give -2), as the number of batches (\(x\)) increases, the cups of raspberries left (\(y\)) decreases.

Answer:

negative