Question
Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
yequals4xplus13
yequalsnegative 4xplus5
yequals4xplus13
yequalsnegative 4xplus5
Answers
Answered by
GPT-4o mini
To determine the relationship between the two lines given by the equations \( y = 4x + 13 \) and \( y = -4x + 5 \), we need to examine their slopes.
1. **Identify the slopes**:
- The slope of the first line \( y = 4x + 13 \) is \( m_1 = 4 \).
- The slope of the second line \( y = -4x + 5 \) is \( m_2 = -4 \).
2. **Check for parallelism**:
- Lines are parallel if their slopes are equal: \( m_1 = m_2 \).
- Here, \( 4 \) is not equal to \( -4 \), so the lines are not parallel.
3. **Check for perpendicularity**:
- Lines are perpendicular if the product of their slopes equals \(-1\): \( m_1 \cdot m_2 = -1 \).
- Here, \( 4 \cdot (-4) = -16 \), which is not equal to \(-1\).
From the analysis, we conclude that the graphs of the equations \( y = 4x + 13 \) and \( y = -4x + 5 \) are **neither parallel nor perpendicular**.
1. **Identify the slopes**:
- The slope of the first line \( y = 4x + 13 \) is \( m_1 = 4 \).
- The slope of the second line \( y = -4x + 5 \) is \( m_2 = -4 \).
2. **Check for parallelism**:
- Lines are parallel if their slopes are equal: \( m_1 = m_2 \).
- Here, \( 4 \) is not equal to \( -4 \), so the lines are not parallel.
3. **Check for perpendicularity**:
- Lines are perpendicular if the product of their slopes equals \(-1\): \( m_1 \cdot m_2 = -1 \).
- Here, \( 4 \cdot (-4) = -16 \), which is not equal to \(-1\).
From the analysis, we conclude that the graphs of the equations \( y = 4x + 13 \) and \( y = -4x + 5 \) are **neither parallel nor perpendicular**.