# Are the set of points C(1, -1), D(3, 4), E(5, 8) are collinear?

Jun 20, 2015

No - the slope of a line through $\left(1 , - 1\right)$ and $\left(3 , 4\right)$ is $\frac{5}{2}$ while the slope of a line through $\left(3 , 4\right)$ and $\left(5 , 8\right)$ is $2$, so there is no one straight line that passes through all three.

#### Explanation:

If a line passes through $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ then its slope m is given by the formula:

$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

So a line through $\left(1 , - 1\right)$ and $\left(3 , 4\right)$ has slope:

$\frac{4 - \left(- 1\right)}{3 - 1} = \frac{5}{2}$

and a line through $\left(3 , 4\right)$ and $\left(5 , 8\right)$ has slope:

$\frac{8 - 4}{5 - 3} = \frac{4}{2} = 2$