Solve for y given y = 5x + 7 (a) x = 5 (b) x = 20. Solve for x given y = 2x − 5 (a) y = 11 (b) y = 37. Find the formula for the table: x | 1 | 2 | 3 | 4, y | 5 | 9 | 13 | 17.

The value of $y$ is $\boxed{\text{32}}$.

b)

The value of $y$ is $\boxed{\text{107}}$.

2. Given $y = 2x - 5$.

a)

The value of $x$ is $\boxed{\text{8}}$.

b)

The value of $x$ is $\boxed{\text{21}}$.

3. Study the following table and determine the formula: Input ($x$) | 1 | 2 | 3 | 4 Output ($y$) | 5 | 9 | 13 | 17

The difference between consecutive $y$ values is $9-5=4$, $13-9=4$, $17-13=4$. This indicates a linear relationship of the form $y = mx + c$, where $m$ is the common difference.
So, $m = 4$. The formula is $y = 4x + c$.

Let's use $(x, y) = (1, 5)$.

The formula is $\boxed{y = 4x + 1}$.