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To solve this worksheet, let’s address each equation step by step. Here's the breakdown:

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### Equation 1: \( y = 5x + 7 \)
**Table of Values**
1. When \( x = -1 \):
   \[
   y = 5(-1) + 7 = -5 + 7 = 2
   \]
2. When \( x = 1 \):
   \[
   y = 5(1) + 7 = 5 + 7 = 12
   \]

**Answers in the table:**
- \( y = 2 \) when \( x = -1 \)
- \( y = 12 \) when \( x = 1 \)

**Question: What is the value of \( y \) when \( x = -1 \) and \( x = 1 \)?**
- \( y = 2 \) when \( x = -1 \)
- \( y = 12 \) when \( x = 1 \)

---

### Equation 2: \( y = 2x + 3 \)
**Table of Values**
1. When \( y = 9 \):
   \[
   9 = 2x + 3 \implies 2x = 9 - 3 = 6 \implies x = 3
   \]

**Answers in the table:**
- \( x = 3 \) when \( y = 9 \)

**Question: What is the value of \( x \) when \( y = 13 \)?**
   \[
   13 = 2x + 3 \implies 2x = 13 - 3 = 10 \implies x = 5
   \]
- \( x = 5 \) when \( y = 13 \)

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### Equation 3: \( y + 12 = 6x \)
Rewriting: \( y = 6x - 12 \)

**Table of Values**
1. When \( x = 2 \):
   \[
   y = 6(2) - 12 = 12 - 12 = 0
   \]

**Answers in the table:**
- \( y = 0 \) when \( x = 2 \)

**Question: What is the value of \( y \) when \( x = 2 \)?**
- \( y = 0 \)

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Would you like these answers or explanations in more detail? Here are some related follow-up questions:

1. Can I assist you in double-checking these calculations?
2. Would you like a plot of these equations to visualize the solutions?
3. Are there any other points from these equations you'd like solved?
4. Would you like a general explanation of how to solve for \( x \) or \( y \) in linear equations?
5. Do you need help filling the full table of values for these equations?

**Tip:** For equations like these, always start by isolating the variable you need and substitute values systematically!

Determine the missing values in the table of values for the equations: y = 5x + 7, y = 2x + 3, and y + 12 = 6x. Also, answer specific questions about y when x = -1 and 1, x when y = 13, and y when x = 2.

Learn to solve linear equations and fill in the table of values for y = 5x + 7, y = 2x + 3, and y + 12 = 6x. Includes step-by-step calculations for x and y values, suitable for Grades 6-8.

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