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:

$m=\frac{1}{2}$

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

$\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ \frac{1}{2}=\frac{y-8}{0-2} \end{gathered}$

and we solve for y so:

$\begin{gathered} -\frac{2}{2}=y-8 \\ -1+8=y \\ 7=y \end{gathered}$

So the equation of the perpendicular line will be:

$y=\frac{1}{2}x+7$