Answer
Yes.
Work Step by Step
Step 1. Given $A(0,-7), B(-3,5), C(2,-15)$, for $AB$, we have $m_1=\frac{-7-5}{0-(-3)}=-4$
Step 2. For $BC$, we have $m_2=\frac{5-(-15)}{-3-2}=-4$
Step 3. For $AC$, we have $m_3=\frac{-7-(-15)}{0-2}=-4$
Step 4. Since $m_1=m_2=m_3$, the three points are collinear.