<u>ANSWER:
</u>
The slope intercept form of the required line is y = -2x + 20.
<u>SOLUTION:
</u>
Given, line equation is ![$y=\frac{1}{2} x-8$](https://tex.z-dn.net/?f=%24y%3D%5Cfrac%7B1%7D%7B2%7D%20x-8%24)
And, Perpendicular line to the given line passes through (7,-6).
We need to find the slope intercept form of perpendicular line of given line.
We already have the point (7, -6) but we need to find the slope.
Now, we know that, product of slopes of two perpendicular lines equals to -1.
Slope of given line is
, by comparing with the general form of slope intercept form.
slope of required line = -1
Slope of perpendicular line = -2
Now, line equation of perpendicular line in point slope form is
![$y-y_{1}=m\left(x-x_{1}\right)$](https://tex.z-dn.net/?f=%24y-y_%7B1%7D%3Dm%5Cleft%28x-x_%7B1%7D%5Cright%29%24)
y – (-6) = -2(x – 7)
y + 6 = -2x + 14
y = -2x + 20
the above equation is in the form of slope intercept form of a line equation
where slope m = -2 and intercept c = 20
hence, the slope intercept form of the required line is y = -2x + 20.