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

2/3

3/2

1/2

2

1 answer

To find the constant of proportionality from the graph, we can examine the points that are given. The line passes through the points (0, 0), (2, 3), and (4, 6).

The constant of proportionality can be determined by the slope of the line, which is calculated using the formula: \[ \text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (2, 3) and (0, 0) to calculate the slope: \[ \text{slope} = \frac{3 - 0}{2 - 0} = \frac{3}{2} \]

The constant of proportionality is equal to this slope, which is \(\frac{3}{2}\).

Therefore, the correct answer is: 3/2