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Let's work through the problem step by step. We are given two linear equations and asked to determine their point of intersection by graphing.

**Line 1: \( y = 2x + 4 \)**  
This equation is in slope-intercept form (\( y = mx + b \)), where:
- \( m = 2 \) (slope)
- \( b = 4 \) (y-intercept)

So, Line 1 has:
- A y-intercept at \( (0, 4) \)
- A slope of 2, meaning for every 1 unit increase in \( x \), \( y \) increases by 2 units.

**Line 2: \( y = -2x + 8 \)**  
Again, this is in slope-intercept form with:
- \( m = -2 \) (slope)
- \( b = 8 \) (y-intercept)

So, Line 2 has:
- A y-intercept at \( (0, 8) \)
- A slope of -2, meaning for every 1 unit increase in \( x \), \( y \) decreases by 2 units.

### Finding the Point of Intersection:
To find the point of intersection, we can set the two equations equal to each other:

\[
2x + 4 = -2x + 8
\]

Solving for \( x \):

1. Add \( 2x \) to both sides:
   \[
   2x + 2x + 4 = 8
   \]
   \[
   4x + 4 = 8
   \]

2. Subtract 4 from both sides:
   \[
   4x = 4
   \]

3. Divide by 4:
   \[
   x = 1
   \]

Now, substitute \( x = 1 \) back into one of the original equations to find \( y \). Using Line 1:

\[
y = 2(1) + 4 = 6
\]

Thus, the point of intersection is \( (1, 6) \).

### Conclusion:
- The two lines intersect at the point \( (1, 6) \).
  
Would you like further details or help with graphing?

Here are 5 follow-up questions based on the problem:
1. How do you graph lines using the slope-intercept form?
2. What does the slope tell you about the steepness and direction of a line?
3. How can you check whether two lines are parallel or perpendicular?
4. How does changing the slope affect the graph of a line?
5. Can two lines with the same slope intersect at any point?

**Tip**: When graphing, always start by plotting the y-intercept, then use the slope to find other points on the line.

Graph the lines y = 2x + 4 and y = -2x + 8 to determine the point of intersection.

Learn how to graph the lines y = 2x + 4 and y = -2x + 8 and find their point of intersection with a step-by-step solution. This problem covers key algebraic concepts, including graphing linear equations and finding intersections using slope-intercept form.

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