A line is perpendicular to the line 4x-5y+2=0 and passes through the point (- 5, k) and (-3, - 4) determine the value of k

Answer 1

4x-5y +2 = 0

5y =-4x-2

y = -4x/5 -2/5 slope = -4/5, slope of a perpendicular line is 5/4

y=5x/4 + b. to calculate b plug in the point (-3,-4)

-4 = 5(-3)/4 + b

b =-4 +15/4 = -1/4

b=-1/4

y=5x/4 -1/4 if it also goes through the point, (-5,k) plug that point in to solve for k

k=5(-5)/4 -1/4 = -25/4-1/4 =-26/4 =-13/2

k =-13/2 =-6.5

k=-6.5 It might help to graph the lines and points