Question

question
what is an equation of the line that passes through the point (-8, -6) and is perpendicular to the line 4x - y = 6?

Explanation:

Step1: Find slope of given line

Rewrite $4x - y = 6$ to slope-intercept form $y=mx+b$:
$y = 4x - 6$, so slope $m_1 = 4$.

Step2: Find perpendicular slope

Perpendicular slope $m_2 = -\frac{1}{m_1} = -\frac{1}{4}$.

Step3: Use point-slope form

Point-slope formula: $y - y_1 = m_2(x - x_1)$ with $(x_1,y_1)=(-8,-6)$:
$y - (-6) = -\frac{1}{4}(x - (-8))$

Step4: Simplify to slope-intercept form

Simplify the equation:
$y + 6 = -\frac{1}{4}(x + 8)$
$y + 6 = -\frac{1}{4}x - 2$
$y = -\frac{1}{4}x - 8$

Answer:

$y = -\frac{1}{4}x - 8$ (or in standard form: $x + 4y = -32$)