1. **Stating the problem:** We have an elastic band initially 20 cm long. Each increase in force by 1 newton increases the length by 0.125 cm. We want to: A) Find the equation relating length to force and provide a graph. B) Find the force at which the band snaps at length 27.6 cm. 2. **Formula and explanation:** The relationship between length $L$ and force $F$ is linear because the length increases steadily with force. This fits the form: $$L = mF + c$$ where $m$ is the rate of increase in length per unit force, and $c$ is the initial length when force is zero. 3. **Finding $m$ and $c$:** - Initial length $c = 20$ cm (when $F=0$). - Increase in length per newton $m = 0.125$ cm/N. So the equation is: $$L = 0.125F + 20$$ 4. **Graph:** The graph is a straight line with slope 0.125 and y-intercept 20, showing length $L$ on the vertical axis and force $F$ on the horizontal axis. 5. **Finding the snapping force:** Given the band snaps at length $L = 27.6$ cm, substitute into the equation: $$27.6 = 0.125F + 20$$ Subtract 20 from both sides: $$27.6 - 20 = 0.125F$$ $$7.6 = 0.125F$$ Divide both sides by 0.125: $$F = \frac{7.6}{0.125} = 60.8$$ So, the band snaps when the force reaches 60.8 newtons. **Final answers:** - Equation relating length to force: $$L = 0.125F + 20$$ - Snapping force: $$F = 60.8$$ newtons