1. **State the problem:** We need to find an equation for the total amount of money $y$ the teacher spends on pencils as a function of the number of students $x$. 2. **Analyze the problem:** - The teacher buys 2 pencils per student, so total pencils for students is $2x$. - He buys 10 additional pencils. - Each pencil costs 0.10 dollars. 3. **Write the total number of pencils:** $$\text{Total pencils} = 2x + 10$$ 4. **Calculate total cost:** Multiply total pencils by cost per pencil: $$y = 0.10 \times (2x + 10)$$ 5. **Simplify the expression:** $$y = 0.10 \times 2x + 0.10 \times 10$$ $$y = 0.20x + 1.0$$ 6. **Interpretation:** The total cost $y$ increases by 0.20 dollars for each student $x$, plus a fixed cost of 1.0 dollars for the extra pencils. **Final equation:** $$y = 0.20x + 1.0$$