Question

question
which equation represents a line which is perpendicular to the line $7x + 3y = -18$
answer
$y = \frac{7}{3}x + 1$
$y = -\frac{3}{7}x + 2$
$y = \frac{3}{7}x + 5$
$y = -\frac{7}{3}x + 6$
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Explanation:

Step1: Rewrite line to slope-intercept

Rearrange $7x + 3y = -18$ to $y=mx+b$:
$$3y = -7x -18$$
$$y = -\frac{7}{3}x -6$$

Step2: Find perpendicular slope

Perpendicular slope is negative reciprocal of $-\frac{7}{3}$:
$$m_{\perp} = \frac{3}{7}$$

Step3: Match slope to options

Identify the option with slope $\frac{3}{7}$.

Answer:

$y = \frac{3}{7}x + 5$