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.

Question

Identify the constant of proportionality from the graph.

(1 point)
Responses

23
Start Fraction 2 over 3 End Fraction

12
Start Fraction 1 over 2 End Fraction

32
Start Fraction 3 over 2 End Fraction

2
2
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Answer 1

To determine the constant of proportionality from the graph defined by the points (0, 0), (2, 3), and (4, 6), we first identify the ratio of \( y \) to \( x \) for the given points.

The constant of proportionality \( k \) can be found using the formula:

\[ k = \frac{y}{x} \]

Let's calculate \( k \) for one of the points, say (2, 3):

\[ k = \frac{3}{2} = 1.5 \]

Now, let's check another point, (4, 6):

\[ k = \frac{6}{4} = \frac{3}{2} \]

Both points give us the same constant of proportionality.

Thus, the constant of proportionality is:

\[ \frac{3}{2} \]

So, the correct response is:

32 \( \frac{3}{2} \)