Use the image to answer the question.
A graph with x-axis and y-axis ranging from 0 to 8 in unit increments shows a line. The line passes through the following plotted points: left parenthesis 0 comma 0 right parenthesis; left parenthesis 2 comma 3 right parenthesis; and left parenthesis 4 comma 6 right parenthesis.
Identify the constant of proportionality from the graph.
(1 point)
Responses
12
Start Fraction 1 over 2 End Fraction
32
Start Fraction 3 over 2 End Fraction
23
Start Fraction 2 over 3 End Fraction
2
The constant of proportionality can be determined by looking at the slope of the line on the graph. The slope is calculated by finding the change in y divided by the change in x between any two points on the line.
Using the given plotted points (0, 0), (2, 3), and (4, 6), we can calculate the slope using the formula:
slope = (change in y) / (change in x)
For the points (0, 0) and (2, 3):
slope = (3 - 0) / (2 - 0) = 3/2 = 1.5
For the points (2, 3) and (4, 6):
slope = (6 - 3) / (4 - 2) = 3/2 = 1.5
Since the slope is constant and equal to 1.5, the constant of proportionality is equal to 1.5.
Therefore, the correct answer is "Start Fraction 3 over 2 End Fraction".