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
2
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1 answer

To find the constant of proportionality from the graph, we need to look at how the y-values relate to the x-values.

A line that represents a relationship in proportionality can be expressed as \( y = kx \), where \( k \) is the constant of proportionality. We can calculate \( k \) using any of the points on the line.

Using the point (2, 3): \[ k = \frac{y}{x} = \frac{3}{2} \]

Using the point (4, 6): \[ k = \frac{y}{x} = \frac{6}{4} = \frac{3}{2} \]

Using the point (0, 0): \[ k = \frac{y}{x} = \frac{0}{0} \] This does not provide information about \( k \).

In all instances where we have valid \( x \) and \( y \) values, the constant of proportionality \( k \) is consistent.

Thus, the constant of proportionality is: \[ \frac{3}{2} \]

So, the correct response is: Start Fraction 3 over 2 End Fraction.