Question

find the equation of a line parallel to $-3x + y = -9$ that passes through the point $(3, -5)$.

answer

$\circ$ $-x - 3y = 12$ \quad \quad $\circ$ $y = -3x - 14$
$\circ$ $-3x - y = -4$ \quad \quad $\circ$ $y = 3x - 14$

Explanation:

Step1: Find slope of given line

Rewrite \(-3x + y = -9\) as \(y = 3x - 9\). Slope (\(m\)) is \(3\) (parallel lines have same slope).

Step2: Use point - slope form

Point - slope formula: \(y - y_1 = m(x - x_1)\), where \((x_1,y_1)=(3,-5)\) and \(m = 3\).
Substitute: \(y - (-5)=3(x - 3)\) → \(y + 5 = 3x - 9\) → \(y = 3x - 14\).

Step3: Verify options

Check which option has slope \(3\) and passes through \((3,-5)\). The option \(y = 3x - 14\) satisfies.

Answer:

\(y = 3x - 14\) (the fourth option: \(y = 3x - 14\))