Question

which function is best represented by this graph?
options:
y = \frac{2}{3}x - 1
y = -\frac{2}{3}x - 1
y = \frac{3}{2}x - 1
y = 3x - 1

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -1)$, so the y-intercept $b=-1$, which matches all options.

Step2: Calculate slope (rise over run)

Pick two points: e.g., $(0, -1)$ and $(3, 1)$. Slope $m=\frac{1 - (-1)}{3 - 0}=\frac{2}{3}$.

Step3: Match to slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=\frac{2}{3}$ and $b=-1$: $y=\frac{2}{3}x - 1$.

Answer:

$y = \frac{2}{3}x - 1$