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
32
Start Fraction 3 over 2 End Fraction
2
2
23
Start Fraction 2 over 3 End Fraction
12
Start Fraction 1 over 2 End Fraction
To find the constant of proportionality, we can calculate the slope of the line that passes through the points (0,0), (2,3), and (4,6).
The slope of a line can be calculated using the formula:
m = (change in y) / (change in x)
From (0,0) to (2,3):
change in y = 3 - 0 = 3
change in x = 2 - 0 = 2
So, the slope from (0,0) to (2,3) is:
m1 = (change in y) / (change in x) = 3/2
From (2,3) to (4,6):
change in y = 6 - 3 = 3
change in x = 4 - 2 = 2
So, the slope from (2,3) to (4,6) is:
m2 = (change in y) / (change in x) = 3/2
Since the slope is constant between all three points, we can conclude that the constant of proportionality is 3/2.
Therefore, the correct answer is: Start Fraction 3 over 2 End Fraction
To find the constant of proportionality from the given graph, we can look at the slope of the line. The slope of a line can be calculated as:
slope = (change in y)/(change in x)
From the plot points, we can see that there is a change in y of 6 units (from 0 to 6) and a change in x of 4 units (from 0 to 4).
So, the slope of the line is:
slope = (6)/(4) = 3/2
Therefore, the constant of proportionality from the graph is 3/2.
To identify the constant of proportionality from the graph, we can analyze the relationship between the x-values and the corresponding y-values of the plotted points.
First, let's find the change in y over the change in x for two consecutive points. We can take the first two points: (0, 0) and (2, 3).
Change in y = 3 - 0 = 3
Change in x = 2 - 0 = 2
The ratio of the change in y to the change in x gives us the constant of proportionality. In this case, it is:
Constant of proportionality = Change in y / Change in x = 3 / 2 = 1.5
So, the correct answer is "Start Fraction 3 over 2 End Fraction", which represents the constant of proportionality from the given graph.