Answer
Yes.
Work Step by Step
Step 1. Given $A(-1,4), B(-2,-1), C(1,14)$, for $AB$, we have $m_1=\frac{-1-4}{-2-(-1)}=5$
Step 2. For $BC$, we have $m_2=\frac{-1-14}{-2-1}=5$
Step 3. For $AC$, we have $m_3=\frac{4-14}{-1-1}=5$
Step 4. Since $m_1=m_2=m_3$, the three points are collinear.
