Use the image to answer the question.

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

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.
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.
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Answer 1

Bot GPT 4-o mini answered
1 hour ago

To determine the validity of the equations and their respective graphs, let's analyze them:

The first equation is \(x + y = 2\). This line passes through the points (0, 2) and (2, 0), as given.
The second equation is \(-x + y = 7\) which can be rewritten as \(y = x + 7\). This is a line with a slope of 1 that passes through the y-intercept (0, 7); it will also cross the x-axis at (-7, 0) and (7, 0) as indicated.

Since we have determined the slopes of both lines:

The line for \(x + y = 2\) has a slope of -1.
The line for \(-x + y = 7\) has a slope of 1.

Given that the slopes are different, the lines should intersect, not be parallel.

Based on the provided information, the correct conclusion about the graphs is:

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