To find the intersection point of the equations \( y = x + 2 \) and \( y = -x + 6 \), we can set the two equations equal to each other:
\[ x + 2 = -x + 6 \]
Now, we can solve for \( x \):
-
Add \( x \) to both sides: \[ 2x + 2 = 6 \]
-
Subtract 2 from both sides: \[ 2x = 4 \]
-
Divide by 2: \[ x = 2 \]
Now that we have \( x = 2 \), we can substitute this value back into either of the original equations to find \( y \). Let's use the first equation \( y = x + 2 \):
\[ y = 2 + 2 = 4 \]
So, the intersection point is \( (2, 4) \).
Thus, the estimated intersection point of the graphs of the given equations is \((2, 4)\).