Question

Which equation represents the same proportional relationship as the graph?

On a coordinate plane, a line goes through points (0, 0), (5, 3), (10, 6).
y = three-fifths x
y = five-thirds x
x y = three-fifths
x y = five-thirds

Answer 1

To determine which equation represents the same proportional relationship as the graph, we can analyze the points provided.

The graph passes through the points (0, 0), (5, 3), and (10, 6).

To find the slope (rate) of the line, we can use two of the given points. Let's take the points (5, 3) and (10, 6):

1. Calculate the change in \( y \) (the vertical change) and the change in \( x \) (the horizontal change):
\[
\Delta y = 6 - 3 = 3
\]
\[
\Delta x = 10 - 5 = 5
\]

2. The slope \( m \) is given by \( \frac{\Delta y}{\Delta x} \):
\[
m = \frac{3}{5}
\]

The relationship between \( y \) and \( x \) in a proportional relationship can be expressed as:
\[
y = mx
\]
Substituting the slope we found:
\[
y = \frac{3}{5}x
\]

Thus, the equation that represents the same proportional relationship as the graph is:
\[
y = \frac{3}{5}x
\]

Looking at your options, the correct choice is:
- \( y = \frac{3}{5}x \)