1. **Problem:** Write an equation in slope-intercept form given slope and y-intercept. Given: slope $m=\frac{3}{5}$, y-intercept $b=6$. Formula: Slope-intercept form is $$y=mx+b$$. Step: Substitute values: $$y=\frac{3}{5}x+6$$ --- 2. **Problem:** Write equation with slope and a point. Given: slope $m=-3$, point $(1,2)$. Formula: Use point-slope form $$y-y_1=m(x-x_1)$$ then convert to slope-intercept. Step: $$y-2=-3(x-1)$$ $$y-2=-3x+3$$ $$y=-3x+3+2$$ $$y=-3x+5$$ --- 3. **Problem:** Write equation through two points. Given points $(4,9)$ and $(2,8)$. Step 1: Find slope: $$m=\frac{9-8}{4-2}=\frac{1}{2}$$ Step 2: Use point-slope form with point $(4,9)$: $$y-9=\frac{1}{2}(x-4)$$ Step 3: Convert to slope-intercept: $$y-9=\frac{1}{2}x-2$$ $$y=\frac{1}{2}x-2+9$$ $$y=\frac{1}{2}x+7$$ --- 4. **Problem:** Convert to slope-intercept form. Given: $$y=3+4(x-1)$$ Step: $$y=3+4x-4$$ $$y=4x-1$$ --- 5. **Problem:** Convert to slope-intercept form. Given: $$y+2=\frac{1}{2}(x+10)$$ Step: $$y+2=\frac{1}{2}x+5$$ $$y=\frac{1}{2}x+5-2$$ $$y=\frac{1}{2}x+3$$ --- 6. **Problem:** Bike rental cost problem. Given: Initial fee plus 1 per hour, 6 hours cost 10. Let equation be $$y=mx+b$$ where $m=1$ (cost per hour), $b$ initial fee. Step 1: Use point $(6,10)$: $$10=1\times6+b$$ $$10=6+b$$ $$b=10-6=4$$ Equation: $$y=1x+4$$ or $$y=x+4$$ Step 2: Cost for 4 hours: $$y=4+4=8$$ Customer pays 8. --- 7. **Problem:** Convert to slope-intercept form. Given: $$-2x+3y=-6$$ Step 1: Solve for $y$: $$3y=2x-6$$ $$y=\frac{2x-6}{3}$$ Step 2: Cancel common factors: $$y=\frac{\cancel{2}x-\cancel{6}}{\cancel{3}}$$ (No common factor between 2 and 3, so no cancellation here, but rewrite as separate terms) $$y=\frac{2}{3}x-2$$ Final answer: $$y=\frac{2}{3}x-2$$