Answer:
8x + 6y + 12 = 0
Explanation:
If n is perpendicular to y=-3/4x +5, its slope is the reciprocal.
The reciprocal is when the fraction is flipped and neg/pos is switched.
m = -3/4 => m=4/3
Substitute m=4/3 and point (9,10) into the equation of a line in slope-intercept
y = mx + b
10 = (4/3)(9) + b
10 = 36/3 + b
10 = 12 + b
b = -2
Slope of the line in slope-intercept form is y = 4/3x -2
To convert slope-intercept form to standard form:
y = mx + b
y = (-ax - c)/b <=this is a different b
ax + by + c = 0
y = 4/3x -2
-2 = -c/b
(4/3) = -a/b
for the equation to work we can set b=6.
-c/b = -2
-c/6 = -2
-c/6 = -12/6
c = 12
4/3 = -a/b
4/3 = -a/6
-a = 8
a = 8
8x + 6y + 12 = 0