Question 288136
First recall that perpendicular lines have slopes that are the negative reciprocal of each other.
In other words, if one of the lines has a slope{{{m = 1/3}}}, then the slope of the perpendicular line is{{{m = -3}}}.
In your problem, you are given the line{{{y = (1/2)x-2}}} whose slope{{{m = 1/2}}}. The new perpendicular line will then have a slope{{{m = -2}}}, so using the slope-intercept form of the linear equation, we have:
{{{y = -2x+b}}} To find the value of b (the y-intercept), substitute the x- and y-coordinates of the origin (0, 0).
{{{y = -2x+b}}} Substitute x = 0 and y = 0.
{{{0 = -2(0)+b}}} so b = 0.
The final equation will be:
{{{highlight(y = -2x)}}}