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Question

2 of 52 of 5 Items

Question
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

Both graphs are correct. 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 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.

Answer 1

To determine the correctness of the graphs presented and the relationship between the equations \(x + y = 2\) and \(-x + y = 7\), we can analyze their characteristics.

1. The equation \(x + y = 2\) represents a line with a slope of -1 (since the equation can be rewritten as \(y = -x + 2\)).

   • It will pass through the points (0, 2) and (2, 0), which matches the description provided of the solid line.

2. The equation \(-x + y = 7\) can be rewritten as \(y = x + 7\), which has a slope of 1.

   • This equation represents a line that passes through points such as (-7, 0) and (7, 14).

Since the slopes of \(x + y = 2\) (slope -1) and \(-x + y = 7\) (slope 1) are different, these two lines will intersect at one point and are not parallel.

Given this analysis, the correct response would be:

The graph of \(x + y = 2\) is correct. The graph of \(-x + y = 7\) is incorrect. The lines should intersect.

Since this option isn't stated explicitly in your provided responses, I would suggest using the response stating that the graph of \(-x + y = 7\) is incorrect and that the lines should intersect, as that aligns best with the explanations above.