Are the lines y=7x+2 and x+7y=8 parallel, perpendicular, or neither?
Understand the Problem
The question is asking us to determine the relationship between the two provided lines, specifically if they are parallel, perpendicular, or neither. We will find their slopes to compare them.
Answer
The relationship between the lines is determined by comparing their slopes. If $m_1 = m_2$, they are parallel; if $m_1 \cdot m_2 = -1$, they are perpendicular; otherwise, they are neither.
Answer for screen readers
The relationship between the two lines depends on their slopes.
Steps to Solve
- Identify the equations of the lines
Let's denote the equations of the two lines given as follows:
Line 1: $y = m_1x + b_1$
Line 2: $y = m_2x + b_2$
Here, $m_1$ and $m_2$ are the slopes of Line 1 and Line 2, respectively.
- Determine the slopes of both lines
From the equations, we can see that the slope of Line 1 is $m_1$ and the slope of Line 2 is $m_2$.
- Compare the slopes
To determine the relationship:
- If $m_1 = m_2$, the lines are parallel.
- If $m_1 \cdot m_2 = -1$, the lines are perpendicular.
- If neither condition is met, then the lines are neither parallel nor perpendicular.
The relationship between the two lines depends on their slopes.
More Information
Understanding the relationship between the slopes of two lines is crucial in geometry and algebra. Parallel lines have the same slope, while perpendicular lines have slopes that multiply to -1. This concept is widely used in various applications, such as in engineering and physics.
Tips
- Forgetting to check both conditions for parallel and perpendicular lines could lead to incorrect conclusions about their relationship. Always verify both conditions carefully.
