1. **State the problem:** We need to determine if the point $(6,-4)$ lies on the line given by the equation $y = -3x + 14$. 2. **Recall the formula:** A point $(x,y)$ lies on the line $y = mx + b$ if substituting $x$ into the equation yields the corresponding $y$ value. 3. **Substitute the point's $x$ value:** Substitute $x=6$ into the equation: $$y = -3(6) + 14$$ 4. **Calculate the right side:** $$y = -18 + 14 = -4$$ 5. **Compare with the point's $y$ value:** The calculated $y$ is $-4$, which matches the point's $y$ coordinate. 6. **Conclusion:** Since the point satisfies the equation, $(6,-4)$ lies on the line $y = -3x + 14$.