y=4/3x +38/3
1) For perpendicular lines they have reciprocal slopes multiplied by -1
So our new equation is going to have a slope of m =4/3 in comparison to m=-3/4 from y=-3/4x-2
2) Writing the slope-intercept form equation:
y=mx+b
y=4/3x+b Plugging into the point
6=4/3(-5) +b
6=-20/3 +b Flipping it
b-20/3=6
b=6+20/3 Calculating the LCM of 1 and 3 and simplifying
b=38/3
y=4/3x +38/3 That's the perpendicular line to the y=-3/4x-2.