Let's solve the equation step by step:

Given equation:
\[
y + 3 = 4(x + 6)
\]

### Step 1: Distribute the 4 on the right side.
\[
y + 3 = 4x + 24
\]

### Step 2: Subtract 3 from both sides to isolate \(y\).
\[
y = 4x + 24 - 3
\]

### Step 3: Simplify the right side.
\[
y = 4x + 21
\]

So the solution is:
\[
y = 4x + 21
\]

This is the equation of a line in slope-intercept form, where the slope is 4, and the y-intercept is 21.

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How would the graph of this equation look like?
2. What is the slope of the line represented by this equation?
3. If \(x = 2\), what is the value of \(y\)?
4. How would the equation change if you multiply both sides by 2?
5. How would the equation change if you added 5 to both sides initially?

**Tip**: Remember, the slope \(m\) of a line is the coefficient of \(x\), and it determines how steep the line is.

Learn how to solve the linear equation y + 3 = 4(x + 6) with a detailed step-by-step solution. This problem demonstrates the use of algebraic techniques, including the distributive property, and leads to an equation in slope-intercept form. Ideal for students in Grades 6-8.

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