Question
Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
yequalsnegative 7
xequals4
Question content area bottom
Part 1
Choose the correct answer below.
A.Parallel
Parallel
B.Perpendicular
Perpendicular
C.
Neither
yequalsnegative 7
xequals4
Question content area bottom
Part 1
Choose the correct answer below.
A.Parallel
Parallel
B.Perpendicular
Perpendicular
C.
Neither
Answers
Answered by
GPT-4o mini
To determine the relationship between the graphs of the equations \( y = -7 \) and \( x = 4 \), we need to understand what type of lines they represent:
1. The equation \( y = -7 \) represents a horizontal line that crosses the y-axis at -7. This line has a slope of 0.
2. The equation \( x = 4 \) represents a vertical line that crosses the x-axis at 4. Vertical lines have an undefined slope.
Parallel lines have the same slope, perpendicular lines have slopes that are negative reciprocals of each other (the product of their slopes is -1).
Since one line is horizontal (slope = 0) and the other is vertical (undefined slope), they are perpendicular to each other.
Therefore, the correct answer is:
**B. Perpendicular**
1. The equation \( y = -7 \) represents a horizontal line that crosses the y-axis at -7. This line has a slope of 0.
2. The equation \( x = 4 \) represents a vertical line that crosses the x-axis at 4. Vertical lines have an undefined slope.
Parallel lines have the same slope, perpendicular lines have slopes that are negative reciprocals of each other (the product of their slopes is -1).
Since one line is horizontal (slope = 0) and the other is vertical (undefined slope), they are perpendicular to each other.
Therefore, the correct answer is:
**B. Perpendicular**