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To graph the equation \( y + 4 = 4(x - 2) \), let's first simplify the equation into the slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Simplify the equation
We start with:
\[
y + 4 = 4(x - 2)
\]
Distribute the 4 on the right-hand side:
\[
y + 4 = 4x - 8
\]
Now, subtract 4 from both sides to solve for \( y \):
\[
y = 4x - 8 - 4
\]
\[
y = 4x - 12
\]

### Step 2: Identify the slope and y-intercept
The equation is now in the form \( y = 4x - 12 \), where:
- The slope \( m = 4 \).
- The y-intercept \( b = -12 \).

### Step 3: Plot the graph
1. Start by plotting the y-intercept, \( (0, -12) \). However, based on the grid provided, we might not see this point because it's off the visible section of the graph.
2. Use the slope \( m = 4 \), which means for every 1 unit you move to the right on the x-axis, you move 4 units up on the y-axis.

From the point where the graph is visible, you can move up 4 units for every step to the right.

Would you like help with the next steps in plotting the graph, or any further details on this? Here are some questions to extend your understanding:

1. How can you find the x-intercept of a line given its equation?
2. What happens to the graph if the slope is negative?
3. How would the graph change if the y-intercept was positive?
4. Can you explain how to graph a vertical or horizontal line?
5. How does the steepness of the slope affect the appearance of the line?

**Tip:** Always check if points of interest, like intercepts, fall within the range of your graph grid.

Learn how to graph the linear equation y + 4 = 4(x - 2) by converting it to slope-intercept form. Understand the concepts of slope and y-intercept with easy-to-follow steps for middle and high school students.

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