Given:
Equation of line is [tex]y=\dfrac{1}{4}x-7[/tex].
The perpendicular line passes through (-2,-6).
To find:
The point slope form of perpendicular line.
Solution:
We have,
[tex]y=\dfrac{1}{4}x-7[/tex]
On comparing this equation with [tex]y=mx+b[/tex], we get
[tex]m=\dfrac{1}{4}[/tex]
Slope of given line is [tex]\dfrac{1}{4}[/tex].
Product of slopes of two perpendicular of the lines is -1.
So, [tex]Slope\times \dfrac{1}{4}=-1[/tex]
[tex]Slope=-4[/tex]
Slope of required line is -4 and it passes through (-2,-6). So, the point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope.
[tex]y-(-6)=-4(x-(-2))[/tex]
[tex]y+6=-4(x+2)[/tex]
Therefore, the correct option is A.
