1. **State the problem:** We are given a linear function $R(x)$ representing the cost in dollars to rent a room for $x$ hours. We need to find $R(4)$ and interpret its meaning. 2. **Identify the function:** From the graph description, the line starts just above 200 dollars at 0 hours and goes just below 950 dollars at 19 hours. We can estimate the function $R(x)$ as a linear function of the form: $$R(x) = mx + b$$ where $m$ is the slope and $b$ is the y-intercept (cost at 0 hours). 3. **Find the y-intercept $b$:** The graph shows the cost at 0 hours is just above 200 dollars. Let's approximate $b = 210$. 4. **Find the slope $m$:** The cost increases from about 210 dollars at 0 hours to about 940 dollars at 19 hours. Calculate slope: $$m = \frac{940 - 210}{19 - 0} = \frac{730}{19} = 38.42$$ 5. **Write the function:** $$R(x) = 38.42x + 210$$ 6. **Calculate $R(4)$:** $$R(4) = 38.42 \times 4 + 210 = 153.68 + 210 = 363.68$$ 7. **Interpretation:** The value $R(4) = 363.68$ means that renting the room for 4 hours costs approximately 364 dollars. **Final answers:** (a) $R(4) = 363.68$ (b) Renting the room for 4 hours costs 364 dollars.