1. We are asked to find a linear function $f(x)$ such that $f(0) = 7$ and $f(3) = 1$. 2. A linear function has the form $$f(x) = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. Since $f(0) = 7$, substituting $x=0$ gives $$f(0) = m \cdot 0 + b = b = 7.$$ So, $b = 7$. 4. Next, use the point $(3,1)$ to find $m$: $$1 = m \cdot 3 + 7$$ 5. Solve for $m$: $$1 - 7 = 3m$$ $$-6 = 3m$$ $$m = \frac{-6}{3}$$ $$m = -2$$ 6. Therefore, the linear function is: $$f(x) = -2x + 7$$ This function passes through the points $(0,7)$ and $(3,1)$ as required.