Answer
$$\color {blue}{\bf\text{No, the points are not collinear}}$$
Work Step by Step
For clarity lets start by naming our points:
$A=(-7,4)$
$B=(6,-2)$
$C=(-1,1)$
First, we'll use the distance formula for the distance between each pair of points:
$d(P,Q)=\sqrt{(x_{P}-x_{Q})^2+(y_{P}-y_{Q})^2}$
$AB= \sqrt{(-7-6)^2+(4-(-2))^2}$
$AB= \sqrt{(-13)^2+6^2}$
$AB= \sqrt{169+36}$
$AB= \sqrt{205}$
$AC= \sqrt{(-7-(-1))^2+(4-1)^2}$
$AC= \sqrt{(-6)^2+3^2}$
$AC= \sqrt{36+9}$
$AC= \sqrt{45}$
$BC= \sqrt{(6-(-1))^2+(-2-1 )^2}$
$BC= \sqrt{7^2+(-3 )^2}$
$BC= \sqrt{49+9}$
$BC= \sqrt{58}$
Now that we have the lengths of the sides,
$AB= \sqrt{205}$, $AC= \sqrt{45}$, $BC=\sqrt{58}$,
we can see if the two shortest equal the longest.
$\sqrt{58}+\sqrt{45}=\sqrt{205}$
Which is $\bf \text{False}$, so:
$$\color {blue}{\bf\text{No, the points are not collinear}}$$
