1. **State the problem:** We are given two systems of equations and asked to graph them and choose the correct graph. The first system is: $$c = 0.5n + 1.5$$ $$c = 10$$ The second system is: $$c = 0.5n - 1$$ $$c = 10$$ 2. **Analyze the first system:** - The first equation is a line with slope $0.5$ and y-intercept $1.5$. - The second equation is a horizontal line where $c = 10$. 3. **Find points for the first line:** - When $n=0$, $c = 0.5(0) + 1.5 = 1.5$. - When $n=20$, $c = 0.5(20) + 1.5 = 10 + 1.5 = 11.5$. So the first line passes through points $(0,1.5)$ and $(20,11.5)$. 4. **Analyze the second system:** - The first equation is a line with slope $0.5$ and y-intercept $-1$. - The second equation is again a horizontal line where $c = 10$. 5. **Find points for the second line:** - When $n=0$, $c = 0.5(0) - 1 = -1$. - When $n=20$, $c = 0.5(20) - 1 = 10 - 1 = 9$. 6. **Check the horizontal line $c=10$:** - This line passes through points $(0,10)$ and $(20,10)$. 7. **Compare with the options:** - Option A shows one line passing through $(0,1.5)$ and $(20,11.5)$ and the other line passing through $(0,10)$ and $(20,10)$. - This matches the first system. - Option B shows one line passing through $(0,1.5)$ and $(20,11.5)$ and the other line passing through $(0,0)$ and $(20,10)$, which does not match the horizontal line $c=10$. - Options C and D do not match the points from either system. **Final answer:** The correct graph is option A.