+191 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)
+118673 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}
+191 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!
