A line through the points $(2, -9)$ and $(j, 17)$ is parallel to the line $2x + 3y = 21$. What is the value of $j$?
To find the value of $j$, I need to use the fact that parallel lines have the same slope. I can find the slope of the line $2x + 3y = 21$ by rewriting it in slope-intercept form: $y = -\frac{2}{3}x + 7$. The slope of this line is $-\frac{2}{3}$. I can also find the slope of the line through $(2, -9)$ and $(j, 17)$ by using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$. Plugging in the coordinates, I get: $m = \frac{17 - (-9)}{j - 2}$. Simplifying, I get: $m = \frac{26}{j - 2}$. Since the slopes are equal, I can set them equal to each other and solve for $j$: $-\frac{2}{3} = \frac{26}{j - 2}$. Subtracting 4 from both sides, I get: $-2j = 74$. Dividing both sides by -2, I get: $j = -37$. 