Question

which of the following is the correct graph of the equation $y = -\frac{3}{2}x + 4$?

Explanation:

Step1: Analyze the slope and y-intercept

The equation is \( y = -\frac{3}{2}x + 4 \). The slope \( m = -\frac{3}{2} \) (negative, so the line should decrease from left to right) and the y-intercept \( b = 4 \) (the line crosses the y-axis at \( (0, 4) \)).

Step2: Eliminate incorrect options

• Option B and D have positive slopes (lines increasing from left to right), so eliminate them.
• Option A has a y-intercept below 0, but we need a y-intercept at 4. Eliminate A.
• Option C has a negative slope and a y-intercept at \( (0, 4) \), matching the equation.

Answer:

C (the graph labeled C)