To determine which set of equations represents the two lines graphed, we can analyze the equations in each option based on their slopes and y-intercepts.
-
Option A: \( y = x + 2 \) (slope = 1, y-intercept = 2) and \( y = x - 4 \) (slope = 1, y-intercept = -4)
- Both lines are parallel (same slope), so they wouldn't intersect.
-
Option B: \( y = x + 2 \) (slope = 1, y-intercept = 2) and \( y = -x - 4 \) (slope = -1, y-intercept = -4)
- These lines have opposite slopes, indicating they will intersect.
-
Option C: \( y = -x + 2 \) (slope = -1, y-intercept = 2) and \( y = x - 4 \) (slope = 1, y-intercept = -4)
- These lines also have opposite slopes, indicating they will intersect.
-
Option D: \( y = x - 2 \) (slope = 1, y-intercept = -2) and \( y = -x - 4 \) (slope = -1, y-intercept = -4)
- These lines have opposite slopes, indicating they will intersect.
-
Option E: \( y = -x + 2 \) (slope = -1, y-intercept = 2) and \( y = -x - 4 \) (slope = -1, y-intercept = -4)
- Both lines are parallel (same slope), so they wouldn't intersect.
Now, if the graph shows two lines that intersect, the possible options would be:
- B
- C
- D
To narrow it down to which particular equations correspond to the specific graph you referred to (if provided graphically), we would need details about the slopes and y-intercepts, or the intersection point.
From the available information, if you can provide the specific features of the lines (such as their intersections), we can definitively conclude which option represents the set of equations for the two lines graphed.