The graph of the proportional relationship between the number of sit-ups and the time taken is a straight line passing through the origin (0,0) with a slope of 2/3.
The number of sit-ups a student can do in 60 seconds = 40
The number of sit-ups the student can do in 150 seconds = 100
For the given data points: (60, 40) and (150, 100)
You can calculate the constant of proportionality (k) using the formula k = y/x: k = 40/60 = 2/3; 100/150 = 2/3.
Alternatively, we can determine the constant of proportionality or slope using m = (y₂ - y₁)/(x₂ - x₁)
= (100 - 40)/(150 - 60)
= 60/90
= 2/3
To graph the proportional relationship between the number of sit-ups and the time taken, you can use a coordinate plane. The x-axis represents the time taken in seconds, and the y-axis represents the number of sit-ups.
We can use the above constant of proportionality to find other points on the graph, like (30, 20) and (90, 60)
We plot these points on the coordinate plane and connect them with a straight line. As a proportional relationship, the graph line passes through the origin (0,0).
|
120 |-
|
100 |- o
| /
80 |- /
| /
60 | - o
| /
40 |-
|_____________
60 150
Thus, the graph of the proportional relationship between the number of sit-ups and the time taken will be a straight line passing through the origin with a slope of 2/3. This graph is the best I can provide.