Line Equation F24274

1. **State the problem:** Find the equation of the line passing through the points $(-2,43)$, $(1,10)$, and $(5,22)$. 2. **Check if points are collinear:** A single line can only pass through all three points if they are collinear. We check this by comparing slopes between pairs of points. 3. **Formula for slope between two points:** $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 4. **Calculate slope between $(-2,43)$ and $(1,10)$:** $$m_1 = \frac{10 - 43}{1 - (-2)} = \frac{-33}{3} = -11$$ 5. **Calculate slope between $(1,10)$ and $(5,22)$:** $$m_2 = \frac{22 - 10}{5 - 1} = \frac{12}{4} = 3$$ 6. Since $m_1 = -11$ and $m_2 = 3$, the slopes are not equal, so the points are not collinear. 7. **Conclusion:** No single line passes through all three points. Therefore, there is no equation of a line passing through $(-2,43)$, $(1,10)$, and $(5,22)$ simultaneously.