Questions: Question 6 Determine if the lines are parallel, perpendicular, or neither. y=7x+8 and y=7x-15 Parallel Perpendicular Neither I don't know

Solution Steps

To determine if the lines are parallel, perpendicular, or neither, we need to compare their slopes. The given equations are in the slope-intercept form \( y = mx + b \), where \( m \) is the slope. If the slopes are equal, the lines are parallel. If the product of the slopes is -1, the lines are perpendicular. Otherwise, they are neither.

1. Extract the slopes from both equations.
2. Compare the slopes to determine if the lines are parallel, perpendicular, or neither.

The equations of the lines are given as: \[ y = 7x + 8 \quad \text{(Line 1)} \] \[ y = 7x - 15 \quad \text{(Line 2)} \] From these equations, we can identify the slopes:

• For Line 1, the slope \( m_1 = 7 \).
• For Line 2, the slope \( m_2 = 7 \).

To determine the relationship between the two lines, we compare their slopes:

• Since \( m_1 = m_2 \), we have \( 7 = 7 \).

Since the slopes of both lines are equal, we conclude that the lines are parallel.

Final Answer