+0  
 
+4
86
5
avatar+108 

The three points $(3,-5)$, $(-a + 2, 3)$, and $(2a+3,2)$ lie on the same line. What is $a$?

 

(I don't know how to do this since the I don't know the slope in this question)

 Aug 19, 2021
 #1
avatar+114818 
+2

You do not know what the slop is but you do know that the slope between any two points will be the same as between any other 2 points.

 

\(\frac{3--5}{-a+2-3}=\frac{2--5}{2a+3-3}\\ \frac{8}{-a-1}=\frac{7}{2a}\\~\\ 16a=-7a-7\\ 23a=-7\\ a=\frac{-7}{23} \)

 

 

 

check

\((3,-5),\quad (2\frac{7}{23},3),\quad (2\frac{9}{23},2)\)

 

 

 

LaTex:

\frac{3--5}{-a+2-3}=\frac{2--5}{2a+3-3}\\
\frac{8}{-a-1}=\frac{7}{2a}\\~\\
16a=-7a-7\\
23a=-7\\
a=\frac{-7}{23}

 Aug 19, 2021
edited by Melody  Aug 19, 2021
 #2
avatar+108 
-1

Thank you very much.

 

I'm actually not that confident working with slopes and lines sometimes because I'm more familiar with equations than graphs.

 

Still, thanks!

OrangeJuicy  Aug 19, 2021
 #3
avatar+114818 
+1

I didn't use the graph.

The graph was just checking that the algebra was correct.

 

Slope is just rise over run

 

Rise is just the difference in y values and run is the difference in x values.  Easy peazy.

 

(just be careful about the negatives.)

Melody  Aug 19, 2021

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