Question

find the equation of the line perpendicular to $y = -\frac{7}{4}x - 5$, that passes through (7, 6).
$y = \frac{?}{\quad}x + \quad$

Explanation:

Step1: Find perpendicular slope

The slope of the given line is $m_1 = -\frac{7}{4}$. The slope of a perpendicular line is the negative reciprocal: $m_2 = \frac{4}{7}$.

Step2: Solve for y-intercept

Substitute $m=\frac{4}{7}$, $x=7$, $y=6$ into $y=mx+b$.
$$6 = \frac{4}{7}(7) + b$$
$$6 = 4 + b$$
$$b = 6-4 = 2$$

Answer:

$y = \frac{4}{7}x + 2$