Question

what equation represents the proportional relationship displayed in the table?
x: 1, 5, 8, 10
y: 15, 75, 120, 150
enter your answer by filling in the box to complete the equation
y = __ x
options: 10, 3, 15, 5

Explanation:

Step1: Find constant of proportionality

For proportional relationships, $k = \frac{y}{x}$. Use the first pair $(x=1, y=15)$:
$\frac{15}{1} = 15$

Step2: Verify with other pairs

Check $(x=5, y=75)$: $\frac{75}{5} = 15$; $(x=8, y=120)$: $\frac{120}{8} = 15$; $(x=10, y=150)$: $\frac{150}{10} = 15$

Step3: Write the equation

Proportional equations are $y = kx$, substitute $k=15$.

Answer:

$\boldsymbol{y = 15x}$
Correct option: $\boldsymbol{\bigcirc \ 15}$