+0  
 
0
30
1
avatar

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

Best Answer 

 #1
avatar+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
Sort: 

1+0 Answers

 #1
avatar+5552 
+1
Best Answer

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

23 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details