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
2
2
23
Start Fraction 2 over 3 End Fraction
32
Start Fraction 3 over 2 End Fraction
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1 answer
To find the constant of proportionality from the given points on the line (0,0), (2,3), and (4,6), we can use the definition of proportionality: the constant of proportionality \( k \) can be found by using the formula:
\[ k = \frac{y}{x} \]
Using the point (2, 3):
\[ k = \frac{3}{2} \]
Using the point (4, 6):
\[ k = \frac{6}{4} = \frac{3}{2} \]
Since both calculations give us the same result, the constant of proportionality is:
\[ \frac{3}{2} \]
Thus, the answer is \( \frac{3}{2} \).
