1. **State the problem:** We are given input-output pairs: inputs $5,6,7,8$ and outputs $11,14,17,20$. We want to find the expression (function) that relates the input $x$ to the output $y$. 2. **Identify the pattern:** Notice the outputs increase by $3$ each time: $14-11=3$, $17-14=3$, $20-17=3$. This suggests a linear function of the form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** Using two points $(5,11)$ and $(6,14)$, slope is $$m = \frac{14 - 11}{6 - 5} = \frac{3}{1} = 3.$$ 4. **Find the intercept $b$:** Substitute $m=3$ and one point, say $(5,11)$, into $y=3x + b$: $$11 = 3 \times 5 + b \implies 11 = 15 + b \implies b = 11 - 15 = -4.$$ 5. **Write the expression:** The function is $$y = 3x - 4.$$ 6. **Verify:** Check with another input, $x=7$: $$y = 3 \times 7 - 4 = 21 - 4 = 17,$$ which matches the given output. **Final answer:** $$\boxed{y = 3x - 4}$$