Answer:
D. [tex]y-7=\frac{1}{4}(x+2)[/tex]
Step-by-step explanation:
The point-slope form of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]
The line given to us has equation; [tex]y=-4x+8[/tex].
The slope of this line is -4. The of the line perpendicular to this line is the negative reciprocal of the slope of the given line.
Our slope of interest is therefore; [tex]m=\frac{1}{4}[/tex]
Since the point goes through (-2,7), we have [tex]x_1=-2,y_1=7[/tex].
We plug in the slope and the point into the point-slope formula to obain;
[tex]y-7=\frac{1}{4}(x--2)[/tex]
The required equation is:
[tex]y-7=\frac{1}{4}(x+2)[/tex]
