Question

match the equation with the correct graph\\
$f(x) = -\frac{3}{2}x + 1$

Explanation:

Step1: Identify slope and y-intercept

The equation $f(x) = -\frac{3}{2}x + 1$ is in slope-intercept form $y=mx+b$, where $m=-\frac{3}{2}$ (negative slope) and $b=1$ (y-intercept at $(0,1)$).

Step2: Analyze graph slopes

Top graph: Positive slope (rises right), does not match $m=-\frac{3}{2}$.
Bottom graph: Negative slope (falls right), matches $m=-\frac{3}{2}$.

Step3: Verify y-intercept

Bottom graph crosses y-axis at $(0,1)$, which matches $b=1$.

Answer:

The correct graph is the bottom one (the line with negative slope passing through $(0,1)$).