Line n is perpendicular to y=-3/4x +5 and goes through point (9,10) write line n in standard form

8x + 6y + 12 = 0

Step-by-step 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