Q.Find the slope of the line passing through $(4, -3)$ and $(-2, 5)$. Hence determine whether the points $(4, -3)$, $(-2, 5)$ and $(10, -11)$ are collinear.

[!TLDR] Slope of $(4,-3)$ to $(-2,5)$ is $-\dfrac{4}{3}$; the slope of $(4,-3)$ to $(10,-11)$ is also $-\dfrac{4}{3}$, so all three points are collinear. [!ANSWER] Slope $=-\dfrac{4}{3}$; the three points are collinear.

Slope through $(4,-3)$ and $(-2,5)$: $m=\dfrac{5-(-3)}{-2-4}=\dfrac{8}{-6}=-\dfrac{4}{3}$. To test collinearity of $(4,-3),(-2,5),(10,-11)$, compute the slope between $(4,-3)$ and $(10,-11)$ as well: $\dfrac{-11-(-3)}{10-4}=\dfrac{-8}{6}=-\dfrac{4}{3}$ — the same value. As a further check, the slope between $(-2,5)$ and $(10,-11)$: $\dfrac{-11-5}{10-(-2)}=\dfrac{-16}{12}=-\dfrac{4}{3}$ also. Since the slope between every pair of the three points agrees, the points lie on one straight line, i.e. they are collinear. [!ANSWER] Slope of the first line $=-\dfrac{4}{3}$; the three given points are collinear.

Compute the slope of the given pair; then compute the slope between one of those points and the third point (and, as a check, the third pair too) and compare.

A common slip is checking the slope of only one extra pair and stopping — always confirm with at least two of the three possible pairs, since one lucky match is not proof for three points.