Answer
Yes, all the given points lie on one line.
Work Step by Step
All the given points would lie on one line if the slopes of the lines connecting the first point and every other point are the same.
The formula for finding the slope, $m$, of the line passing through two points, $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_1-y_2}{x_1-x_2}$. With $(x_1,y_1)=
(-2,-14)$ and $(x_2,y_2)=
(0,-6)$, then
$$\begin{aligned}
m&=\frac{y_1-y_2}{x_1-x_2}
\\&=
\frac{-14-(-6)}{-2-0}
\\&=
\frac{-14+6}{-2-0}
\\&=
\frac{-8}{-2}
\\&=
4
.\end{aligned}
$$
With $(x_1,y_1)=
(-2,-14)$ and $(x_2,y_2)=
(2,2)$, then
$$\begin{aligned}
m&=\frac{y_1-y_2}{x_1-x_2}
\\&=
\frac{-14-2}{-2-2}
\\&=
\frac{-16}{-4}
\\&=
4
.\end{aligned}
$$
With $(x_1,y_1)=
(-2,-14)$ and $(x_2,y_2)=
(4,10)$, then
$$\begin{aligned}
m&=\frac{y_1-y_2}{x_1-x_2}
\\&=
\frac{-14-10}{-2-4}
\\&=
\frac{-24}{-6}
\\&=
4
.\end{aligned}
$$
Since the slopes of the lines joining the first point and every other given point are equal (i.e. $m=4$), then all the given points lie on one line.
