Question
Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
yequalsnothingxplus12
yequalsminusxplus1
Question content area bottom
Part 1
Choose the correct answer below.
yequalsnothingxplus12
yequalsminusxplus1
Question content area bottom
Part 1
Choose the correct answer below.
Answers
Answered by
GPT-4o mini
To determine if the graphs of the two equations are parallel, perpendicular, or neither, we need to find the slopes of the lines represented by each equation.
1. The first equation is \( y = 0x + 12 \).
- Here, the slope (m) is 0.
2. The second equation is \( y = -x + 1 \).
- In this case, the slope (m) is -1.
Now we can analyze the slopes:
- Two lines are **parallel** if they have the same slope.
- Two lines are **perpendicular** if the product of their slopes is -1.
In this case:
- The slopes are 0 (from the first line) and -1 (from the second line).
- Since the slopes are not equal, the lines are not parallel.
- The product of the slopes is \( 0 \times (-1) = 0 \), which is not equal to -1, so the lines are not perpendicular either.
Thus, the conclusion is:
The graphs of the equations are **neither parallel nor perpendicular**.
1. The first equation is \( y = 0x + 12 \).
- Here, the slope (m) is 0.
2. The second equation is \( y = -x + 1 \).
- In this case, the slope (m) is -1.
Now we can analyze the slopes:
- Two lines are **parallel** if they have the same slope.
- Two lines are **perpendicular** if the product of their slopes is -1.
In this case:
- The slopes are 0 (from the first line) and -1 (from the second line).
- Since the slopes are not equal, the lines are not parallel.
- The product of the slopes is \( 0 \times (-1) = 0 \), which is not equal to -1, so the lines are not perpendicular either.
Thus, the conclusion is:
The graphs of the equations are **neither parallel nor perpendicular**.