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
2
2
1/2
Start Fraction 1 over 2 End Fraction
2/3
Start Fraction 2 over 3 End Fraction
3/2
To determine the constant of proportionality from the graph, we can examine the relationship between the y-values and x-values.
Looking at the plotted points (0,0), (2,3), and (4,6), we can see that as the x-values increase by 2 (from 0 to 2 and from 2 to 4), the corresponding y-values also increase by 3 (from 0 to 3 and from 3 to 6).
Therefore, the constant of proportionality is 3/2 (or 1.5).
To identify the constant of proportionality from the graph, we can first observe that the line passes through the points (0, 0), (2, 3), and (4, 6).
The constant of proportionality represents the rate at which the y-coordinate increases or decreases with respect to the x-coordinate. It can be calculated by finding the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line.
In this case, we can calculate the constant of proportionality by considering the change in the y-coordinates and x-coordinates between the points (0, 0) and (2, 3).
The change in the y-coordinate is 3 - 0 = 3, and the change in the x-coordinate is 2 - 0 = 2.
Therefore, the constant of proportionality is 3/2.
So, the correct answer is: 3/2
To identify the constant of proportionality from the graph, we need to determine the relationship between the x-values and the y-values of the plotted points.
From the given information, the points (0,0), (2,3), and (4,6) are plotted on the graph.
To find the constant of proportionality, we can calculate the ratio of the change in y-values to the change in x-values between any two points.
Let's calculate the ratio between the points (0,0) and (2,3):
Change in y-values: 3 - 0 = 3
Change in x-values: 2 - 0 = 2
Ratio = Change in y-values / Change in x-values = 3/2 = 1.5
Similarly, let's calculate the ratio between the points (2,3) and (4,6):
Change in y-values: 6 - 3 = 3
Change in x-values: 4 - 2 = 2
Ratio = Change in y-values / Change in x-values = 3/2 = 1.5
Since the ratios are consistent and equal, the constant of proportionality from the graph is 1.5 or 3/2.