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# Help

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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 $j$?

Guest Dec 7, 2017

#1
+5552
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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

hectictar  Dec 7, 2017
Sort:

#1
+5552
+1

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

hectictar  Dec 7, 2017

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