Question

what is an equation of the line that passes through the point (3, -5) and is parallel to the line 4x + 3y = 9?

Explanation:

Step1: Find slope of given line

Rewrite $4x + 3y = 9$ as $y = -\frac{4}{3}x + 3$, so slope $m = -\frac{4}{3}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $(3, -5)$ and $m$: $y - (-5) = -\frac{4}{3}(x - 3)$.

Step3: Simplify to standard form

$y + 5 = -\frac{4}{3}x + 4$ → Multiply by 3: $3y + 15 = -4x + 12$ → $4x + 3y = -3$.

Answer:

$4x + 3y = -3$