Question

question
find the equation of a line parallel to $4x + y = -9$ that passes through the point $(9, -5)$.
answer
$y = -4x + 31$
$y = 4x + 31$
$4x - y = 41$
$-x + 4y = -29$

Explanation:

Step1: Find slope of given line

Rewrite $4x + y = -9$ to slope-intercept form $y=mx+b$:
$y = -4x -9$, so slope $m=-4$

Step2: Use point-slope form

Parallel lines have equal slopes. Use point $(9,-5)$:
$y - (-5) = -4(x - 9)$

Step3: Simplify to slope-intercept form

$y + 5 = -4x + 36$
$y = -4x + 36 - 5$
$y = -4x + 31$

Step4: Verify matching option

The derived equation matches the first option.

Answer:

$y = -4x + 31$