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Use the image to answer the question.

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 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.
Both graphs are correct. The lines should be parallel.

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.
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1 answer

To analyze the given equations and their graphical representations:

  1. Equations:

    • The first equation is \( x + y = 2 \).
    • The second equation is \( -x + y = 7 \).

  2. Finding the slopes:

    • For the first equation \( x + y = 2 \), rearranging gives \( y = -x + 2 \). The slope is -1.
    • For the second equation \( -x + y = 7 \), rearranging gives \( y = x + 7 \). The slope is +1.

  3. Parallel vs. Intersecting:

    • Since the slopes of the two lines are different (-1 and +1), the lines will intersect.
    • Lines are considered parallel if they have the same slope.

Conclusion:

  • The graph of \( x + y = 2 \) is correct, but the graph of \( -x + y = 7 \) is incorrect because it suggests the lines are parallel when they should in fact be intersecting at one point.

Therefore, the answer is: The graph of −x+y=7 is incorrect. The lines should intersect.