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A graph with the x-axis representing time in minutes ranging from 0 to 10 in increments of 1, and the y-axis representing levels passed ranging from 0 to 10 in increments of 1 shows three lines labeled 1, 2 and 3. Line 1 passes through the following points: left parenthesis 0 comma 2 right parenthesis; left parenthesis 2 comma 5 right parenthesis; and left parenthesis 4 comma 8 right parenthesis. Line 2 passes through the following points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 3 right parenthesis; left parenthesis 4 comma 7 right parenthesis; and left parenthesis 5 comma 8 right parenthesis. Line 3 passes through the following points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 2 right parenthesis; left parenthesis 4 comma 4 right parenthesis; and left parenthesis 7 comma 7 right parenthesis.

Three friends are playing video games. The graph shows the number of levels passed based on amount of time played. Which friend’s graph (1, 2, or 3) is a proportional relationship?

3 answers

Friend 1's graph shows a proportional relationship.
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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.
To find the unit rate, we need to calculate the slope of the line connecting the three points on the graph. The slope represents the change in y (stretch) divided by the change in x (weight).

The given points are:
(2, 10)
(3, 15)
(6, 30)

To find the change in y, we subtract the y-coordinates of the first and last point:
Change in y = 30 - 10 = 20

To find the change in x, we subtract the x-coordinates of the first and last point:
Change in x = 6 - 2 = 4

Therefore, the unit rate (slope) is the change in y divided by the change in x:
Unit rate = Change in y / Change in x = 20 / 4 = 5

So, the unit rate is 5 millimeters per gram.