Answer:
Pair 1: Neither
Pair 2: Parallel
Pair 3: Neither
Explanation:
To determine whether each pair of lines is perpendicular, parallel, or neither, we need to analyze their slopes.
Let's rewrite the given equations in slope-intercept form (y = mx + b) to easily determine the slopes:
4y = 2x - 4
Dividing both sides by 4, we get:
y = (1/2)x - 1
y = 20 + 4
Simplifying, we have:
y = 24
The slope of the first equation is 1/2, and the slope of the second equation is 0 since it is a horizontal line.
Pair 1: The first equation has a non-zero slope, and the second equation has a zero slope. Hence, these lines are neither perpendicular nor parallel.
Next, let's analyze the second pair:
2y = 42 + 4
Simplifying, we have:
y = 23
2y = 42 - 7
Simplifying, we have:
y = 17.5
The slopes of both equations are zero since they are horizontal lines.
Pair 2: Both equations have zero slopes, indicating that the lines are parallel.
Finally, let's examine the last pair:
y = -22 + 9
Simplifying, we have:
y = -13
2y = 42 - 7
Simplifying, we have:
y = 17.5
The slopes of both equations are different, so the lines are neither perpendicular nor parallel.
Pair 3: These lines are neither perpendicular nor parallel.
To summarize the results:
Pair 1: Neither
Pair 2: Parallel
Pair 3: Neither