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Question

A graph with x-axis and y-axis labeled from 0 to 30 in increments of 2. Three points are plotted with a line connecting them.
A graph with x-axis and y-axis labeled from 0 to 30 in increments of 2. Points are plotted at left parenthesis 2 comma 10 right parenthesis, left parenthesis 3 comma 15 right parenthesis, and left parenthesis 6 comma 30 right parenthesis. A line is drawn connecting the three points.

The stretch of a spring in millimeters is proportional to the weight in grams attached to the end of the spring. Find the unit rate.

(1 point)
__mm per gram

Answer 1

To find the unit rate of stretch of the spring in millimeters per gram, we need to examine the relationship between the points plotted on the graph, which represent the stretch of the spring (in mm) and the weight (in grams).

From the points given:

1. The first point is (2, 10) which means that a weight of 2 grams causes a stretch of 10 mm.
2. The second point is (3, 15), which means that a weight of 3 grams causes a stretch of 15 mm.
3. The third point is (6, 30), which means that a weight of 6 grams causes a stretch of 30 mm.

To find the unit rate (mm per gram), we can compute the ratio of stretch to weight for each point:

1. For the first point: \[ \text{Unit rate} = \frac{10 \text{ mm}}{2 \text{ grams}} = 5 \text{ mm/gram} \]

2. For the second point: \[ \text{Unit rate} = \frac{15 \text{ mm}}{3 \text{ grams}} = 5 \text{ mm/gram} \]

3. For the third point: \[ \text{Unit rate} = \frac{30 \text{ mm}}{6 \text{ grams}} = 5 \text{ mm/gram} \]

In all cases, the unit rate is consistent.

Thus, the unit rate of stretch of the spring is: \[ \text{Answer: } 5 \text{ mm per gram} \]