The option that could use both intercepts to produce viable solutions is:
(years of experience, starting salary)
This pair can represent a linear relationship (such as in a salary model) where you can interpret both the y-intercept (starting salary with 0 years of experience) and the x-intercept (the years of experience required to achieve a salary of $0, if applicable).
The other options (temperature vs. car rentals, nominations vs. awards, and age vs. weight) do not lend themselves as clearly to the interpretation of both intercepts in a linear manner.