Does the graph show the system of equations x+y=2 and −x+y=7? Should the lines for the system be parallel?

Question

(1 point)
Responses

The 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.

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.

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.

Both graphs are correct. The lines should be parallel.

Answer 1

To analyze the system of equations given:

1. The first equation is \( x + y = 2 \).
2. The second equation is \( -x + y = 7 \) (which can also be written as \( y = x + 7 \)).

To check if the lines are parallel or if they will intersect, we can rearrange both equations into slope-intercept form (y = mx + b):

1. For \( x + y = 2 \): \[ y = -x + 2 \] (slope = -1, y-intercept = 2)

2. For \( -x + y = 7 \) (or \( y = x + 7 \)): \[ y = x + 7 \] (slope = 1, y-intercept = 7)

Since the slopes of the two lines are different (-1 for the first line and +1 for the second line), the lines will intersect at one point rather than being parallel.

So, the correct response is: The graph of −x+y=7 is incorrect. The lines should intersect.