Question

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals negative x plus 6. The equation of the dotted line is y equals x plus 2. The lines intersect at left parenthesis 2 comma 4 right parenthesis which is not plotted as a point.

Estimate the intersection point of the graphs of the following linear equations in two variables.
y=x+2

y=−x+6

(1 point)
(
)
Remaining Attempts : 3
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Answer 1

To find the intersection point of the two linear equations \( y = x + 2 \) and \( y = -x + 6 \), we need to set the equations equal to each other and solve for \( x \).

1. Set the equations equal:
\[
x + 2 = -x + 6
\]

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

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

4. Divide both sides by 2:
\[
x = 2
\]

5. Now, plug \( x = 2 \) back into either of the original equations to find \( y \). Using \( y = x + 2 \):
\[
y = 2 + 2 = 4
\]

Therefore, the intersection point of the two graphs is \( (2, 4) \).

So the answer is:
\[
(2, 4)
\]