Question

1. which equation represents a line which is perpendicular to the line y = 1/2x+7? a) x + 2y = 2 b) x - 2y=-12 c) 2x + y = 3 d) y - 2x=-5

Explanation:

Step1: Find the slope of the given line

The given line is $y = \frac{1}{2}x + 7$, its slope $m_1=\frac{1}{2}$. For a line perpendicular to it, the slope $m_2$ satisfies $m_1\times m_2=- 1$. So $m_2=-2$.

Step2: Rewrite each option in slope - intercept form $y = mx + b$

Option A:

$x + 2y=2$ can be rewritten as $2y=-x + 2$ or $y=-\frac{1}{2}x + 1$, slope $m =-\frac{1}{2}$.

Option B:

$x-2y=-12$ can be rewritten as $-2y=-x - 12$ or $y=\frac{1}{2}x+6$, slope $m=\frac{1}{2}$.

Option C:

$2x + y = 3$ can be rewritten as $y=-2x + 3$, slope $m=-2$.

Option D:

$y-2x=-5$ can be rewritten as $y=2x - 5$, slope $m = 2$.

Answer:

C. $2x + y = 3$