Question

which equation represents the graphed function?
$y = -3x + 3$
$y = 3x - 3$
$y = 3x - \frac{1}{3}$
$y = -\frac{1}{3}x + 3$

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 3)$, so $b=3$.

Step2: Calculate slope

Use points $(0,3)$ and $(3,2)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{2-3}{3-0}=-\frac{1}{3}$

Step3: Write linear equation

Use slope-intercept form $y=mx+b$
$y=-\frac{1}{3}x+3$

Answer:

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