https://file.aiquickdraw.com/mathbot/file/1726238860122la65qcix.jpg

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:

| Input Values (X) | 10  | -0.5  | 25  | 4   | 15  |
|------------------|-----|-------|-----|-----|-----|
| Output Values (Y) | 136 | 10    | 316 | 64  | 196 |

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.

Use the function y = 12x + 16 to complete the table of x and y values: (Input: 10, B, 25, D, 15; Output: A, 10, C, 64, E).

Solve the linear equation y = 12x + 16 and complete a table of x and y values. Learn how to substitute x and solve for y, and how to reverse the process to find missing values for x when given y. Suitable for middle school students, Grades 6-8.

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