1. **Graph the function** $-5x + 2y = -10$. Step 1: Rewrite in slope-intercept form $y = mx + b$. $$-5x + 2y = -10 \implies 2y = 5x - 10 \implies y = \frac{5}{2}x - 5$$ Step 2: Identify slope $m = \frac{5}{2}$ and y-intercept $b = -5$. Step 3: Plot the y-intercept $(0, -5)$ and use slope to find another point: rise 5, run 2. 2. **Graph the function** $3x - 6y = 12$. Step 1: Rewrite in slope-intercept form. $$3x - 6y = 12 \implies -6y = -3x + 12 \implies y = \frac{1}{2}x - 2$$ Step 2: Slope $m = \frac{1}{2}$, y-intercept $b = -2$. Step 3: Plot $(0, -2)$ and use slope to find another point: rise 1, run 2. 3. **Graph the function** $y - 3 = -\frac{2}{5}(10x - 5)$. Step 1: Distribute the right side. $$y - 3 = -\frac{2}{5} \times 10x + \frac{2}{5} \times 5 = -4x + 2$$ Step 2: Add 3 to both sides. $$y = -4x + 2 + 3 = -4x + 5$$ Step 3: Slope $m = -4$, y-intercept $b = 5$. Step 4: Plot $(0, 5)$ and use slope to find another point: down 4, right 1. 4. **Simplify into standard form** the expression: $$(5x^2 - 4 + 6x) - (8x + 4x^2 + 1)$$ Step 1: Remove parentheses. $$5x^2 - 4 + 6x - 8x - 4x^2 - 1$$ Step 2: Combine like terms. $$5x^2 - 4x^2 + 6x - 8x - 4 - 1 = (5x^2 - 4x^2) + (6x - 8x) + (-4 - 1) = x^2 - 2x - 5$$ 5. **Solve the formula** $S = 4F - 24$ for $F$. Step 1: Add 24 to both sides. $$S + 24 = 4F$$ Step 2: Divide both sides by 4. $$F = \frac{S + 24}{4}$$ **Final answers:** 1. $y = \frac{5}{2}x - 5$ 2. $y = \frac{1}{2}x - 2$ 3. $y = -4x + 5$ 4. $x^2 - 2x - 5$ 5. $F = \frac{S + 24}{4}$