Write the equation of the line that passes through the point $P ( 0,0 )$ and is perpendicular to the line $y = -$ $4 x + 10$.
A) $\quad y = 4 x$
B) $y = - \frac { 1 } { 4 } x + 10$
C) $y = \frac { 1 } { 4 } x$
D) $\quad y = - 10 x$
E) $y = - \frac { 1 } { 10 } x$

Question

Quizplus · Accepted Answer

The slope of the given line is $-4$, so the slope of the line perpendicular to it is $\frac{-1}{-4}=\frac{1}{4}$. We also know that the line passes through point $(0,0)$, so using the point-slope formula we get $$y-0=\frac{1}{4}(x-0) \Rightarrow y=\frac{1}{4}x$$ Thus the equation of the line that passes through point $P(0,0)$ and is perpendicular to the given line is $\boxed{	extbf{(C) } y=\frac{1}{4}x}$.

Write the Equation of the Line That Passes Through the Point