Use the image to answer the 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
The unit rate for the stretch of the spring is mm per gram.
To find the unit rate, we need to determine the amount of stretch per gram of weight.
By looking at the graph, we can see that the weight (in grams) is plotted on the x-axis, and the stretch (in millimeters) is plotted on the y-axis.
The three points on the graph are: (2, 10), (3, 15), and (6, 30).
To calculate the stretch per gram, we can take any two points on the line and find the change in y (stretch) divided by the change in x (weight).
Let's choose the points (2, 10) and (6, 30):
Change in y = 30 - 10 = 20 mm
Change in x = 6 - 2 = 4 grams
So, the unit rate is:
20 mm / 4 grams = 5 mm/gram
Therefore, the unit rate is 5 mm/gram.
To find the unit rate, we need to calculate the ratio of the change in the stretch of the spring to the change in weight.
Looking at the graph, we can see that the points (2, 10), (3, 15), and (6, 30) are plotted.
To calculate the change in the stretch, we subtract the initial stretch from the final stretch. In this case, the initial stretch is 10 mm (at 2 grams) and the final stretch is 30 mm (at 6 grams). So, the change in stretch is 30 mm - 10 mm = 20 mm.
Similarly, to calculate the change in weight, we subtract the initial weight from the final weight. Here, the initial weight is 2 grams and the final weight is 6 grams. So, the change in weight is 6 grams - 2 grams = 4 grams.
Now, we can find the unit rate by dividing the change in stretch by the change in weight. Therefore, the unit rate is 20 mm / 4 grams = 5 mm per gram.
Hence, the answer is "5 mm per gram".