1. **State the problem:** Michaela's mom wants to find the number of hours at which two plumber companies charge the same total amount. 2. **Identify variables:** Let $x$ = number of hours of labor. Let $y$ = total cost charged by a company. 3. **Write the equations using $y = mx + b$:** - First company: $y = 36x + 50$ - Second company: $y = 39x + 35$ 4. **Set the two equations equal to find $x$:** $$36x + 50 = 39x + 35$$ 5. **Solve for $x$:** Subtract $36x$ from both sides: $$50 = 3x + 35$$ Subtract 35 from both sides: $$15 = 3x$$ Divide both sides by 3: $$x = 5$$ 6. **Interpretation:** At $5$ hours of labor, both companies will charge the same amount. 7. **Find the total cost at $x=5$:** Using first company: $$y = 36(5) + 50 = 180 + 50 = 230$$ **Final answer:** The two companies charge the same amount after 5 hours, and the cost will be 230.