1. **State the problem:** We are given the total cost function for a home security system: $$C = 80 + 40x$$ where $C$ is the total cost and $x$ is the number of months of service. 2. **Understand the function:** This is a linear function with a fixed installation fee of 80 and a monthly fee of 40 per month. 3. **Graphing the function for $x \leq 50$:** - The y-intercept (when $x=0$) is $C = 80$. - The slope is 40, meaning the cost increases by 40 for each additional month. 4. **Check the values at key points:** - At $x=0$, $C=80$. - At $x=50$, $C=80 + 40 \times 50 = 80 + 2000 = 2080$. 5. **Interpret the graph:** The graph is an upward sloping line starting at 80 on the cost axis and increasing by 40 for each month up to 50 months. 6. **Address the user's note about the graph:** The user mentioned a downward sloping line with negative slope, but the function $C=80+40x$ has a positive slope of 40, so the graph should slope upward, not downward. **Final answer:** The graph of $C=80+40x$ for $x \leq 50$ is a straight line starting at $(0,80)$ and increasing to $(50,2080)$ with a positive slope of 40.