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

 Dec 21, 2021
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Parallel lines have the same slope.

This means that we will have a 2x+3y term on the left side of the new equation, since this yields a slope of -2/3. If 2x+3y=a, and (2,-9) is a solution, then 2*2 + 3*-9 = a, so a=-23. 

Inputting x=j and y=-17 into 2x+3y=-23, we have 2j = -23 + 51 = 28, so j=14. 

 Dec 21, 2021

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