Question

Identify an equation in point-slope form for the line perpendicular to y = 1/4 x - 7 that passes through (-2,-6)

Answer 1

$\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\\text{We have}\ y=\dfrac{1}{4}x-7\to m_1=\dfrac{1}{4}.\\\\\text{therefore}\ m_2=-\dfrac{1}{\frac{1}{4}}=-4.\\\\\text{The point-slope form}:\ y-y_1=m(x-x_1).\\\\\text{Substitute the value of a slope and coordinates of the point (-2, -6)}:\\\\y-(-6)=-4(x-(-2))\\\\Answer:\ \boxed{C.\ y+6=-4(x+2)}$