Question

which graph and equation shows a proportional relationship between x and y?
y = 2x - 1.5
graph
y = 0.45x
graph
y = x + 1.5
graph
y = 4.5
graph

Explanation:

Step1: Recall proportional relationship rule

A proportional relationship between $x$ and $y$ follows the form $y = kx$, where $k$ is a constant, and its graph passes through the origin $(0,0)$.

Step2: Analyze each option

• For $y=2x-1.5$: This is in $y=mx+b$ form with $b=-1.5

eq0$, so not proportional.

• For $y=0.45x$: This matches $y=kx$ (with $k=0.45$), and its graph passes through the origin, so this is proportional.
• For $y=x+1.5$: This is in $y=mx+b$ form with $b=1.5

eq0$, so not proportional.

• For $y=4.5$: This is a horizontal line, not in $y=kx$ form, so not proportional.

Answer:

The graph and equation $y=0.45x$ (top-right option) shows a proportional relationship between $x$ and $y$.