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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

3/2
Start Fraction 3 over 2 End Fraction

2/3
Start Fraction 2 over 3 End Fraction

1/2
Start Fraction 1 over 2 End Fraction

2
2
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Answer 1

To identify the constant of proportionality from the graph, we can use the form of a linear equation \(y = kx\), where \(k\) is the constant of proportionality.

From the given points:

• The first point is (0, 0), which confirms that the line passes through the origin.
• The second point is (2, 3).
• The third point is (4, 6).

We can calculate the constant of proportionality using the points (2, 3) and (4, 6) as follows:

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

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

Since both calculations yield the same constant of proportionality, we find that the constant of proportionality is \( \frac{3}{2} \).

Therefore, the answer is: 3/2 (Start Fraction 3 over 2 End Fraction)