Question

Does the graph show the system of equations x+y=2 and −x+y=7? Should the lines for the system be parallel?(1 point)ResponsesThe graph of −x+y=7 is incorrect. The lines should intersect.The graph of negative x plus y equals 7 is incorrect. The lines should intersect.Both graphs are correct. The lines should be parallel.Both graphs are correct. The lines should be parallel.The graph of −x+y=7 is incorrect. The lines should be parallel.The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.The graph of x+y=2 is incorrect. The lines should intersect.The graph of x plus y equals 2 is incorrect. The lines should intersect.

Answer 1

To determine whether the lines represented by the equations \( x + y = 2 \) and \( -x + y = 7 \) are parallel, we can compare their slopes.

1. **Convert both equations to slope-intercept form (y = mx + b)**:

- For \( x + y = 2 \):
\[
y = -x + 2
\]
The slope (m) is \(-1\).

- For \( -x + y = 7 \):
\[
y = x + 7
\]
The slope (m) is \(1\).

2. **Compare the slopes:**
- The first line has a slope of \(-1\), and the second line has a slope of \(1\). Since the slopes are different, the lines are not parallel; they will intersect.

Therefore, the correct response is: **The graph of \( -x + y = 7 \) is incorrect. The lines should intersect.**