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

23
Start Fraction 2 over 3 End Fraction

32
Start Fraction 3 over 2 End Fraction

2

Answer 1

To find the constant of proportionality from the given points, we need to determine the relationship between the x-values and y-values. The constant of proportionality \( k \) can be defined as \( k = \frac{y}{x} \).

Let's calculate \( k \) using the points provided:

1. For the point \( (0, 0) \), we cannot determine a proportionality because \( y = 0 \) when \( x = 0 \).
2. For the point \( (2, 3) \):
\[
k = \frac{y}{x} = \frac{3}{2}
\]
3. For the point \( (4, 6) \):
\[
k = \frac{y}{x} = \frac{6}{4} = \frac{3}{2}
\]

In both cases (from \( (2, 3) \) and \( (4, 6) \)), the constant of proportionality is \( \frac{3}{2} \).

Therefore, the correct response is \( \frac{3}{2} \).