Question

Write an equation in slope-intercept form for the line that is perpendicular to y = −14x + 2 and passes through the point (-4, 3)

Answer 1

$k:y=m_1x+b_!\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\ \iff\ m_1m_2=-1$

We have

$k:y=-14x+2$

$l:y=mx+b$

$l\ \perp\ k\ \iff\ -14m=-1\qquad|:(-14)\to m=\dfrac{1}{14}$

Therefore

$l:y=\dfrac{1}{14}x+b$

We know: the line l passes through the point (-4, 3).

Substitute the coordinates of the point to the equation of a line l:

$3=\dfrac{1}{14}\cdot(-4)+b\\\\3=\dfrac{1}{7}\cdot(-2)+b\\\\3=-\dfrac{2}{7}+b\qquad|+\dfrac{2}{7}\\\\b=3\dfrac{2}{7}$

Answer: $y=\dfrac{1}{14}x+3\dfrac{2}{7}$