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# I know this may not be hard but I'm having some problems

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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

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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
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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
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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