Question

the equation of the line that is perpendicular to the line y - 4x= -2 (x -3 )and passes through the point (2, 8)

Answer 1

if the line is perpendicular to:

`y-4=-2(x-3)`

so the slope will be the negative reciproc of this exuation so:

`m=(1)/(2)`

Now with the slope and the coordinate (2,8) we can find the intersection c whrn x = 0 so

`\begin{gathered} m=(y-y_1)/(x-x_1) \\ (1)/(2)=(y-8)/(0-2) \end{gathered}`

and we solve for y so:

`\begin{gathered} -(2)/(2)=y-8 \\ -1+8=y \\ 7=y \end{gathered}`

So the equation of the perpendicular line will be:

`y=(1)/(2)x+7`