Question

(c) determine whether x and y are proportional
□ proportional
y is □ times x
□ not proportional

Explanation:

Step1: Analyze top graph

Proportional relationships form straight lines passing through the origin $(0,0)$. The top graph's line does not pass through $(0,0)$, so it is not proportional.

Step2: Analyze bottom graph

The bottom graph's line passes through $(0,0)$ and points like $(1,5)$, $(2,10)$, $(3,15)$.

Step3: Calculate the constant

For each point, $\frac{y}{x} = \frac{5}{1} = \frac{10}{2} = \frac{15}{3} = 5$. Since the ratio is constant and the line passes through the origin, $y = 5x$, so it is proportional.

Answer:

1. Top graph: Not proportional
2. Bottom graph: Proportional, $y$ is $5$ times $x$