Question

which graph represents the function $y - 3 = \frac{3}{2}(x - 4)$?

Explanation:

Step1: Rewrite to slope-intercept form

Start with the given point-slope equation:
$y - 3 = \frac{3}{2}(x - 4)$
Distribute $\frac{3}{2}$:
$y - 3 = \frac{3}{2}x - 6$
Add 3 to both sides:
$y = \frac{3}{2}x - 3$

Step2: Identify key features

• Slope: $m = \frac{3}{2}$ (positive, so line rises right)
• y-intercept: $(0, -3)$
• Verify a second point: When $x=2$, $y = \frac{3}{2}(2) - 3 = 0$, so the line passes through $(2, 0)$

Step3: Match to graphs

Look for a line with positive slope, passing through $(0, -3)$ and $(2, 0)$.

Answer:

The first graph (leftmost option, rising line passing through (2, 0) and (0, -3))