Question

Does the graph show the system of equations = + y = 2 and -= + y = 7? Should the
lines for the system be parallel?
(1 point)
• 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+ y = 7 is incorrect. The lines should intersect.
O The graph of -x + y = 7 is incorrect. The lines should be parallel.

Answer 1

To determine whether the lines from the given equations should be parallel or intersect, we need to analyze the equations and their slopes.

The provided equations are:

1. \( x + y = 2 \)
2. \( -x + y = 7 \)

First, we can rearrange these equations into the slope-intercept form \( y = mx + b \):

1. For \( x + y = 2 \):
\[
y = -x + 2
\]
- The slope (m) is \(-1\).

2. For \( -x + y = 7 \):
\[
y = x + 7
\]
- The slope (m) is \(1\).

Since the slopes of the two lines are different (\(-1\) and \(1\)), the lines are not parallel. Instead, they will intersect at some point.

Based on this analysis, the correct conclusion would be:

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

Thus, among the options you provided, the best choice is:

- "The graph of -x + y = 7 is incorrect. The lines should intersect."

However, to be absolutely clear, the lines are supposed to intersect, not be stated as incorrect; rather the statement reflects the understanding that they are indeed correct in terms of intersection.