Respuesta :
ANSWER:
The slope intercept form of the required line is y = -2x + 20.
SOLUTION:
Given, line equation is [tex]$y=\frac{1}{2} x-8$[/tex]
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 [tex]\frac{1}{2}[/tex], by comparing with the general form of slope intercept form.
[tex]\frac{1}{2} \times[/tex] slope of required line = -1
Slope of perpendicular line = -2
Now, line equation of perpendicular line in point slope form is
[tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
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.
