Question

In gym class, a student can do 30 sit-ups in 60 seconds and 90 sit-ups in 180 seconds. Graph the proportional relationship.

Answer 1

To graph the proportional relationship between the number of sit-ups and the time taken, we can use the given data points:

The student can do 30 sit-ups in 60 seconds.

The student can do 90 sit-ups in 180 seconds.

In a proportional relationship, the ratio of the two quantities remains constant. In this case, we can find the constant of proportionality, which is the rate at which the student is doing sit-ups.

The constant of proportionality is calculated as follows:

Constant of Proportionality = (Number of Sit-ups) / (Time in Seconds)

For the first data point (30 sit-ups in 60 seconds):

Constant of Proportionality = 30 / 60 = 0.5 sit-ups per second

For the second data point (90 sit-ups in 180 seconds):

Constant of Proportionality = 90 / 180 = 0.5 sit-ups per second

Since the constant of proportionality is the same for both data points, it confirms that the relationship is indeed proportional.

Now, let's create a graph. On the x-axis, we'll represent time in seconds, and on the y-axis, we'll represent the number of sit-ups. We'll plot the two data points and connect them with a line:

The graph shows a linear relationship where the number of sit-ups is directly proportional to the time in seconds, with a constant rate of 0.5 sit-ups per second.

Answer 2

graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30.

Explanation:

To graph the proportional relationship between the number of sit-ups (y) and the time in seconds (x), using the given data points (60, 30) and (180, 90):

The proportional relationship equation is:

y = (1/2)x

You can use this equation to plot the graph, with time (x) on the x-axis and the number of sit-ups (y) on the y-axis. The line should pass through both points (60, 30) and (180, 90), indicating a proportional relationship.