1. **State the problem:** We need to find the values of $a$ and $b$ in the linear equation $$C = aN + b$$ that models the cost, $C$, in pounds, of making $N$ loaves of bread when $N \geq 50$. The graph shows two points on the line: (50, 40) and (150, 160). 2. **Use the given points:** We can substitute each point into the equation to form two equations: - For $N=50$, $C=40$: $$40 = a \times 50 + b$$ - For $N=150$, $C=160$: $$160 = a \times 150 + b$$ 3. **Set up the system of equations:** $$\begin{cases} 40 = 50a + b \\ 160 = 150a + b \end{cases}$$ 4. **Subtract the first equation from the second to eliminate $b$:** $$160 - 40 = 150a - 50a$$ $$120 = 100a$$ 5. **Solve for $a$:** $$a = \frac{120}{100} = 1.2$$ 6. **Substitute $a=1.2$ into the first equation to find $b$:** $$40 = 50 \times 1.2 + b$$ $$40 = 60 + b$$ $$b = 40 - 60 = -20$$ 7. **Write the final equation:** $$C = 1.2N - 20$$ **Answer:** The values of $a$ and $b$ are $a=1.2$ and $b = -20$.