Question

Use the image to answer the question.
y = -x + 6
y = x + 2
Estimate the intersection point of the graphs of the following linear equations in two variables.
y = x + 2
y = -x + 6
(__)

Answer 1

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 \( x \):

1. Add \( x \) to both sides:
\[
2x + 2 = 6
\]

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

3. 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 \((2, 4)\).