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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.

 Jun 7, 2021
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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 \(j = -37\)

 Jun 7, 2021

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