Question

question
which equation represents a line which is perpendicular to the line $6x + y = -4?$
answer
$circ y = 6x - 5$
$circ y = \frac{1}{6}x + 8$
$circ y = -\frac{1}{6}x - 2$
$circ y = -6x + 5$
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Explanation:

Step1: Rewrite given line to slope-intercept

First, rearrange $6x + y = -4$ to $y = mx + b$ form:
$y = -6x - 4$
The slope $m_1$ of this line is $-6$.

Step2: Find perpendicular slope

Perpendicular slopes are negative reciprocals. Calculate $m_2$:
$m_2 = -\frac{1}{m_1} = -\frac{1}{-6} = \frac{1}{6}$

Step3: Match slope to options

Identify which option has slope $\frac{1}{6}$.

Answer:

$y = \frac{1}{6}x + 8$