Linear Function 3E28E0

1. **State the problem:** We are given three points $(-4,10)$, $(-2,7)$, and $(6,-5)$ on a linear function and need to find which of the given equations matches this relationship. 2. **Recall the formula for a linear function:** The general form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$ using two points:** $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(-4,10)$ and $(-2,7)$: $$m = \frac{7 - 10}{-2 - (-4)} = \frac{-3}{2} = -\frac{3}{2}$$ 4. **Check if the slope matches the options:** The slope is $-\frac{3}{2}$, so the correct equation must have $m = -\frac{3}{2}$. 5. **Find the y-intercept $b$ using one point and the slope:** Using point $(-4,10)$: $$10 = -\frac{3}{2} \times (-4) + b$$ $$10 = 6 + b$$ $$b = 10 - 6 = 4$$ 6. **Write the equation:** $$y = -\frac{3}{2}x + 4$$ 7. **Verify with another point:** Using $(-2,7)$: $$y = -\frac{3}{2} \times (-2) + 4 = 3 + 4 = 7$$ which matches the point. **Final answer:** $$\boxed{y = -\frac{3}{2}x + 4}$$