A line through the points (2, -9) and (j, 17) is parallel to the line 2x + 3y = 21. What is the value of j?

Question

A line through the points (2, -9) and (j, 17) is parallel to the line 2x + 3y = 21. What is the value of j?

Answer 1

2x+3y=21

3y=-2x+21

y=(-2/3)x+7

the line parallel to this line is y=(-2/3)x+b where you have to find the value of b using point (2,-9)

-9=(-2/3)(2)+b

-9+(4/3)=b

b=-7 2/3 or -23/3

y=(-2/3)x-23/3 is the parallel line

use point (j,17)

17=(-2/3)j-23/3

17+23/3=(-2/3)j

24 2/3=(-2/3)j

74/3=(-2/3)j

multiply both sides by (-3/2)

(-3/2)(74/3)=(-3/2)(-2/3)j

simplify both sides

-37=j