Question

1. are lines y = 2x + 3 and y = 2x - 4 parallel, perpendicular, or neither? parallel perpendicular coincident neither

Explanation:

Step1: Recall the slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
For the line \(y = 2x+3\), the slope \(m_1=2\).
For the line \(y = 2x - 4\), the slope \(m_2 = 2\).

Step2: Use the condition for parallel lines

Two lines \(y=m_1x + b_1\) and \(y=m_2x + b_2\) are parallel if \(m_1=m_2\) and \(b_1
eq b_2\).
Since \(m_1 = m_2=2\) and \(b_1 = 3
eq b_2=-4\).

Answer:

Parallel