A linear function p satisfies p(0) = 6 and p(4) = 22. What is the value of p(10)?

The value $p(0) = 6$ is the $y$-intercept. The slope is $\frac{22 - 6}{4 - 0} = 4$, so $p(x) = 4x + 6$. Then $p(10) = 4(10) + 6 = 46$. Check against the other point: $p(4) = 16 + 6 = 22$. Equivalently, $p(10) = p(4) + 4(6) = 22 + 24 = 46$. A common wrong answer is 26, which comes from adding the slope once, $22 + 4$. Another is 40, from forgetting the intercept (computing $4 \times 10$), and a third is 16, the change in output between the two known points. Multiply the slope by the full change in $x$.