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) Responses 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 intersect. The graph of negative x plus y equals 7 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.
The graph of x+y=2 is incorrect. The lines should intersect.
The correct response is: "The graph of x+y=2 is incorrect. The lines should intersect. The graph of −x+y=7 is incorrect. The lines should intersect."
To determine if the lines represented by the equations x+y=2 and −x+y=7 should be parallel or intersect, we can analyze their slopes.
First, let's rewrite the equations in slope-intercept form, which is y = mx + b, where m represents the slope of the line:
For x+y=2:
y = -x + 2
For −x+y=7:
y = x + 7
From these equations, we can see that the slope of the first line is -1 and the slope of the second line is 1.
If two lines have slopes that are equal, then they are parallel. However, in this case, the slopes are different (-1 and 1). Therefore, the lines represented by the equations x+y=2 and −x+y=7 should intersect, not be parallel.
Given this information, the correct response is:
The graph of x+y=2 is incorrect. The lines should intersect.
The graph of −x+y=7 is incorrect. The lines should intersect.