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)
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}
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!