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The given equation is \( y = 6x + 7 \), and you are asked to find the value of \( y \) when \( x = -3 \).

### Step-by-step solution:

1. Substitute \( x = -3 \) into the equation:
   \[
   y = 6(-3) + 7
   \]

2. Simplify:
   \[
   y = -18 + 7
   \]

3. Add:
   \[
   y = -11
   \]

Thus, the value of \( y \) when \( x = -3 \) is \( \mathbf{-11} \).

Would you like more details on any step, or do you have other questions? 

Here are 5 related questions to expand on this:

1. What is the slope of the equation \( y = 6x + 7 \)?
2. How does changing the constant in the equation affect the graph of the line?
3. What is the \( y \)-intercept of the equation \( y = 6x + 7 \)?
4. How do you find the value of \( y \) for different values of \( x \)?
5. Can this equation have multiple solutions for different \( x \) values?

**Tip:** The slope in a linear equation of the form \( y = mx + b \) represents the rate of change, or how much \( y \) changes for each unit increase in \( x \).

Given y = 6x + 7, what is the value of y when x = -3?

Learn how to find the value of y in the linear equation y = 6x + 7 when x = -3. This problem introduces key algebraic concepts and is suitable for students in Grades 6-8.

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