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:j=-37Step-by-step explanation:step 1Find the slope of the given linewe have[tex]2x+3y=21[/tex]Convert to slope intercept formIsolate the variable ysubtract 2x both sides[tex]3y=-2x+21[/tex]divide by 3 both sides[tex]y=-\frac{2}{3}x+7[/tex]The slope is[tex]m=-\frac{2}{3}[/tex]step 2we have the points(2,-9) and (j,17)Find the slopeThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] substitute[tex]m=\frac{17+9}{j-2}[/tex] [tex]m=\frac{26}{j-2}[/tex] Remember thatIf two lines are parallel then their slope are equaltherefore[tex]\frac{26}{j-2}=-\frac{2}{3}[/tex][tex]26(3)=-2(j-2)\\78=-2j+4\\2j=4-78\\2j=-74\\j=-37[/tex]