Question

which linear equation shows a proportional relationship?
\\( y = -2x - \frac{1}{3} \\)
\\( y = \frac{1}{3}x - 1 \\)
\\( y = \frac{5}{6}x \\)
\\( y = 5x + 3 \\)

Explanation:

Step1: Recall proportional linear form

A proportional linear equation follows the form $y = kx$, where $k$ is a non-zero constant (no constant term added/subtracted).

Step2: Analyze each option

• $y=-2x-\frac{1}{3}$: Has a constant term $-\frac{1}{3}$, not proportional.
• $y=\frac{1}{3}x-1$: Has a constant term $-1$, not proportional.
• $y=\frac{5}{6}x$: Matches $y=kx$ with $k=\frac{5}{6}$, no constant term.
• $y=5x+3$: Has a constant term $3$, not proportional.

Answer:

$\boldsymbol{y = \frac{5}{6}x}$