1. **State the problem:** We want to find the equation for the cost $y$ of renting a backhoe for $x$ days, where $x$ is a positive integer and $x \leq 10$. The cost is $270 for the first day and $135 for each additional day. 2. **Understand the cost structure:** - The first day costs $270. - Each additional day (from day 2 to day $x$) costs $135. 3. **Formulate the equation:** - For $x$ days, the number of additional days after the first day is $x - 1$. - The total cost $y$ is the cost of the first day plus the cost of the additional days: $$y = 270 + 135(x - 1)$$ 4. **Simplify the equation:** $$y = 270 + 135x - 135 = 135x + 135$$ 5. **Interpret the result:** - The equation $y = 135x + 135$ matches option D. **Final answer:** $$y = 135x + 135$$