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A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. The dashed line passes through left parenthesis negative 7 comma 0 right parenthesis and left parenthesis 7 comma 0 right parenthesis.

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=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.

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.
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1 answer

To determine the correctness of the graph and if the lines should be parallel, we need to analyze the given equations.

  1. The first equation is \( x + y = 2 \). This can be rearranged into slope-intercept form: \[ y = -x + 2 \] The slope of this line is -1.

  2. The second equation is \( -x + y = 7 \). This can also be rearranged: \[ y = x + 7 \] The slope of this line is +1.

Analysis of slopes:

  • Lines with different slopes intersect.
  • Since the first line has a slope of -1 and the second line has a slope of +1, they are not parallel and will intersect.

Conclusion regarding the options:

  • Since the graphs of the equations \( x + y = 2 \) and \( -x + y = 7 \) are represented by lines that should intersect (due to having different slopes), the options that indicate the lines should be parallel are incorrect.

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