find r so that the line through (2,6) and (-4,r) is parallel to 2x-3y=4

Answer 1

2x - 3y = 4

3y = 2x -4

y = (2/3)x - 4/3 has slope = 2/3

and any parallel line also has the same slope 2/3 = (6-r)/(2+4)= (6-r)/6

cross multiply

6(2) = 3(6-r)

12 = 18-3r

divide by 3

4 = 6-r

r = 6-4 = 2

a parallel line through the point (2,6) also goes through (-4,2) r=2