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=7
is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. 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.

Both graphs are correct. The lines should be parallel.

1 answer

To determine whether the system of equations \( x + y = 2 \) and \( -x + y = 7 \) is represented correctly in the graph, let's analyze both equations:

  1. Graph of \( x + y = 2 \):

    • This equation can be rewritten in slope-intercept form as \( y = -x + 2 \).
    • The y-intercept is \( 2 \) and the x-intercept is \( 2 \). The line passes through the points \( (0, 2) \) and \( (2, 0) \).

  2. Graph of \( -x + y = 7 \):

    • This equation can also be rewritten in slope-intercept form as \( y = x + 7 \).
    • The y-intercept is \( 7 \) and the x-intercept is \( -7 \). The line passes through the points \( (7, 0) \) and \( (-7, 0) \).

Now consider the nature of the lines:

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

Since the slopes are different, the two lines will intersect.

Now, examining the options:

  • The graph of \( x + y = 2 \) is correct, as it matches the points provided.
  • The graph of \( -x + y = 7 \) is incorrect because it should not be horizontally aligned as indicated by the dashed line stretching across the x-axis from \( (-7, 0) \) to \( (7, 0) \).

Thus, the correct response is:

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