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)

OrangeJuicy Aug 19, 2021

#1**+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}

Melody Aug 19, 2021

#2**+2 **

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