+0

0
27
1
+42

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

Jun 7, 2021

Writing 2x+3y=21 in slope-intercept form, we have y=-2/3x+7, meaning the slope is -2/3.  If the line mentioned is parallel, then it must have the same slope.  Thus, the line passes through the points (2, -9) and (j, 17) and has a slope -2/3, directly translating to $$\frac{17-(-9)}{j-2} = -\frac{2}{3}$$.  Solving this equation, the solution is $$j = -37$$