Answer:
To determine the relationships between these lines, let's analyze their slopes.
1. Line 1: y = -3x + 8
The slope of Line 1 is -3.
2. Line 2: 6x + 2y = 6
Rewrite it in slope-intercept form (y = mx + b):
2y = -6x + 6
y = -3x + 3
The slope of Line 2 is -3.
3. Line 3: y = 3x + 2
The slope of Line 3 is 3.
Now, let's compare the slopes of each pair of lines:
- Lines 1 and 2:
The slopes are both -3, which means these lines are parallel.
- Lines 1 and 3:
The slope of Line 1 is -3, and the slope of Line 3 is 3. These slopes are negative reciprocals of each other, which means these lines are perpendicular.
- Lines 2 and 3:
The slope of Line 2 is -3, and the slope of Line 3 is 3. Again, these slopes are negative reciprocals of each other, so these lines are perpendicular.
To summarize:
- Lines 1 and 2 are parallel.
- Lines 1 and 3 are perpendicular.
- Lines 2 and 3 are perpendicular.
Explanation: