Hello,
Any line that is perpendicular to another line has a negative reciprocal of the slope. So the negative reciprocal of -2/3 is 3/2. Now with the new slope, let's pt it in the equation to find the slop-intercept equation BY using point-slope form: y-y1 = m (slope) (x-x1).
If I put the numbers in the equation, it would look like: y+8 = 3/2 (x-4). Let's simplify by distributing 3/2 to the parenthesis: y + 8 = 3/2x - 6.
To get "y" by itself, let's subtract 8 from both sides: y = 3/2x - 14.
So, the equation is now y = 3/2x - 14.
In the box you would write, "-14".
I hope this helps!
May