Question

What is the slope of a line perpendicular to the line whose equation is 4x-2y=-16 Fully simplify your answer.

Answer 1

Two lines are perpendicular if the multiplication of their slopes is equal to -1.

Isolating y from the equation:

`\begin{gathered} 4x-2y=-16 \\ 4x-2y+16=0 \\ 4x+16=2y \\ (4x+16)/(2)=y \\ (4x)/(2)+(16)/(2)=y \\ 2x+8=y \end{gathered}`

The slope of this line is 2. Therefore, the slope of the line perpendicular to this one will be:

`\begin{gathered} m\cdot2=-1 \\ m=-(1)/(2) \end{gathered}`