Question

find the equation that represents the proportional relationship in this graph, for y in terms of x.

Explanation:

Step1: Identify proportional form

Proportional relationships follow $y = kx$, where $k$ is the constant of proportionality.

Step2: Pick a point from the graph

The line passes through $(6, 10)$. Substitute $x=6$, $y=10$ into $y=kx$.
$$10 = k \times 6$$

Step3: Solve for $k$

Rearrange to isolate $k$:
$$k = \frac{10}{6} = \frac{5}{3}$$

Step4: Write the final equation

Substitute $k=\frac{5}{3}$ back into $y=kx$.

Answer:

$y = \frac{5}{3}x$