A line through the points $(2, -9)$ and $(j, 17)$ is parallel to the line $2x + 3y = 21$. What is the value of $j$?
+9466 First let's find the slope of the line 2x + 3y = 21
2x + 3y = 21
Subtract 2x from both sides of the equation.
3y = -2x + 21
Divide through by 3 .
y = - \(\frac23\)x + 7
Now we can see that the slope of this line is - \(\frac23\) . So....
the slope between any two points of a parallel line also = -\(\frac23\)
the slope between (2, -9) and (j, 17) = - \(\frac23\)
\(\frac{17--9}{j-2}\,=\,-\frac23\\~\\ \frac{26}{j-2}\,=\,-\frac23 \\~\\ 26=-\frac23(j-2)\\~\\ -39=j-2\\~\\ -37=j\)
Here's a graph to check this: https://www.desmos.com/calculator/ovina9gch0
+9466 First let's find the slope of the line 2x + 3y = 21
2x + 3y = 21
Subtract 2x from both sides of the equation.
3y = -2x + 21
Divide through by 3 .
y = - \(\frac23\)x + 7
Now we can see that the slope of this line is - \(\frac23\) . So....
the slope between any two points of a parallel line also = -\(\frac23\)
the slope between (2, -9) and (j, 17) = - \(\frac23\)
\(\frac{17--9}{j-2}\,=\,-\frac23\\~\\ \frac{26}{j-2}\,=\,-\frac23 \\~\\ 26=-\frac23(j-2)\\~\\ -39=j-2\\~\\ -37=j\)
Here's a graph to check this: https://www.desmos.com/calculator/ovina9gch0
