Question

Which equation represents a line which is perpendicular to the line y=-1/2x−6?

Answer 1

Answer:

The equation that represents a line that is perpendicular to the given line is;

$y-2x=-1$

Explanation:

Given the equation;

$y=-\frac{1}{2}x-6$

The slope of the given equation is;

$m_1=-\frac{1}{2}$

for two lines to be perpendicular, their slopes must be the negative inverse of each other.

$\begin{gathered} m_1\cdot m_2=-1 \\ m_2=-\frac{1}{m_1} \end{gathered}$

substituting the given slope;

$\begin{gathered} m_2=-\frac{1}{m_1}=-\frac{1}{(-\frac{1}{2})} \\ m_2=-1\times-\frac{2}{1} \\ m_2=2 \end{gathered}$

Therefore, the slope of the perpendicular line must be equal to 2.

From the given answer choices, let us find the equation with a slope of 2;

$\begin{gathered} x-2y=8 \\ y=\frac{1}{2}x-4 \\ m=\frac{1}{2} \end{gathered}$$\begin{gathered} x+2y=4 \\ y=-\frac{1}{2}x+2 \\ m=-\frac{1}{2} \end{gathered}$$\begin{gathered} 2x+y=6 \\ y=-2x+6 \\ m=-2 \end{gathered}$$\begin{gathered} y-2x=-1 \\ y=2x-1 \\ m=2 \end{gathered}$

Therefore, the equation that represents a line that is perpendicular to the given line is;

$y-2x=-1$