Write the equation of the line that passes through the point $P ( 0,0 )$ and is perpendicular to the line $y =$ $10 x + 5$.
A) $y = - \frac { 1 } { 5 } x$
B) $y = - 5 x$
C) $y = 10 x$
D) $\quad y = \frac { 1 } { 10 } x$
E) $\quad y = - \frac { 1 } { 10 } x + 5$

Question

Quizplus · Accepted Answer

The line $y = 10x+5$ has a slope of 10, so the perpendicular line must have a slope of $-\frac{1}{10}$ (since the product of the slopes of perpendicular lines is -1). 
Using the point-slope form of a line with the point $P(0,0)$, the equation of the perpendicular line is 
$y-0=-\frac{1}{10}(x-0)$
which simplifies to 
$y=-\frac{1}{10}x.$
Therefore, the answer is choice D.

Write the Equation of the Line That Passes Through the Point