1. Statement of the problem: Find the equation of the line in slope-intercept form that passes through the points $(-1, 7)$ and $(4, -8)$. 2. Formula: Use the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ and the slope-intercept form $y = mx + b$. 3. Important rules: Subtract coordinates in the same order, simplify fractions to lowest terms, and substitute a known point to solve for $b$. 4. Compute the slope step by step. $$m = \frac{-8 - 7}{4 - (-1)} = \frac{-15}{5} = -3$$ 5. Find the y-intercept by substituting one point into $y = mx + b$. $$7 = -3(-1) + b \Rightarrow 7 = 3 + b \Rightarrow b = 4$$ 6. Final equation and explanation: Therefore the line in slope-intercept form is $y = -3x + 4$. 7. Check with the other point: Substituting $(4, -8)$ gives $$-8 = -3(4) + 4 = -12 + 4 = -8$$ 8. Conclusion: The equation of the line is $y = -3x + 4$.