Question

Parallel/PerpendicularWhat is an equation of the line that passes through the point (6,-1) and isperpendicular to the line 2x-Y=5?

Answer 1

`\begin{gathered} \text{Two lines are perpendicular when:} \\ \text{slope}1\cdot\text{ slope2 = -1} \\ \text{Line 1} \\ 2x-y=5 \\ y=2x-5 \\ \text{slope1 =2} \\ \text{slope}2=(-1)/(slope1) \\ \text{slope}2=-(1)/(2) \\ \text{Line 2} \\ y=-(1)/(2)x+b \\ P(6,-1) \\ -1=-(1)/(2)\cdot(6)+b \\ -1=-3+b \\ b=-1+3 \\ b=2 \\ y=-(1)/(2)x+2 \\ \text{The equation of the line is }y=-(1)/(2)x+2 \end{gathered}`