Our approach will be to write the desired equation in point-slope form, then simplify that to the desired slope-intercept form.
A perpendicular line will have a slope that is the negative reciprocal of the slope of the given line. The slope of the given line is the coefficient of x, which is 4/3. Turn this upside down and give it the opposite sign and you get -3/4. This is the slope of your perpendicular line.
In point-slope form the equation for a line with slope m through point (h, k) can be written
... y = m(x -h) +k
You want a line with m = -3/4 and (h, k) = (8, -8). We can simply fill in these values to get your line in point-slope form.
... y = (-3/4)(x -8) +(-8)
Now, we can eliminate parentheses to put this into the slope-intercept form you need.
... y = (-3/4)x +6 -8 . . . . use the distributive property. Then collect terms to get ...
... y = (-3/4)x -2
_____
The attached graph shows this line goes through the given point and is perpendicular to the given line.
