The given function is:

$y = 12x + 16$

We will use this equation to find the missing values in the table. Here's how we will proceed:

1. When $x = 10$:

$y = 12(10) + 16 = 120 + 16 = 136$ So, $A = 136$.

2. When $y = 10$:

$10 = 12x + 16$ Subtract 16 from both sides:

$-6 = 12x \implies x = -\frac{6}{12} = -\frac{1}{2}$ So, $B = -0.5$.

3. When $x = 25$:

$y = 12(25) + 16 = 300 + 16 = 316$ So, $C = 316$.

4. When $y = 64$:

$64 = 12x + 16$ Subtract 16 from both sides:

$48 = 12x \implies x = \frac{48}{12} = 4$ So, $D = 4$.

5. When $x = 15$:

$y = 12(15) + 16 = 180 + 16 = 196$ So, $E = 196$.

Final Table:

Would you like more details or clarifications on any part of this?

Here are five follow-up questions:

1. What would the output be for $x = 20$?
2. Can you describe how the slope of the function affects the output values?
3. If the equation were $y = 12x + 20$, how would the results change?
4. How would you solve for $x$ if $y = 100$?
5. Can you plot the function $y = 12x + 16$ on a graph?

Tip: When solving for unknowns in linear equations, always isolate the variable by performing inverse operations step by step.