What is the missing value of f(5)?

A linear function changes at a constant rate. From $x = 1$ to $x = 3$, the input rises by 2 and the output rises by $15 - 7 = 8$, so the rate of change is $\frac{8}{2} = 4$ per unit. Going from $x = 3$ to $x = 5$ is another increase of 2 in the input, so the output rises by another 8: $f(5) = 15 + 8 = 23$. A common wrong answer is 19, from adding the slope 4 once rather than multiplying by the change of 2 in the input. Another is 31, from continuing the pattern in the wrong table row by adding 16. Always multiply the slope by the full change in $x$.