Ask a New Question
Menu

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=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.
Skip to navigation

1 answer

To determine whether the graph represents the system of equations \( x+y=2 \) and \( -x+y=7 \), let's analyze each equation:

  1. For the equation \( x + y = 2 \):

    • The solid line passes through the points \( (0, 2) \) and \( (2, 0) \).
    • Rearranging gives \( y = -x + 2 \). This is a linear equation with a slope of -1.

  2. For the equation \( -x + y = 7 \):

    • The dashed line passes through the points \( (-7, 0) \) and \( (7, 0) \), which suggests that this line is horizontal (constant y-value).
    • Rearranging gives \( y = x + 7 \), which indicates a slope of +1, but looking at the coordinates, it seems that is not the correct description based on the stated line being horizontal passing through \( y=0 \).

Since the solid line has a slope of -1 and passes through \( y=2 \) at \( x=0 \), and the dashed line appears horizontal along \( y=0 \), these lines should not be parallel. Therefore, they should intersect.

Given the above analysis, the first equation is represented correctly, but the second evidence suggests that the equation of the dashed line does NOT correspond to \( -x + y = 7 \) as described in the problem.

Thus, the correct response would be: The graph of \( -x + y = 7 \) is incorrect. The lines should intersect.