Are the lines represented by the equations \(y = 4x + 2\) and \(y = 4x - 7\) parallel, perpendicular, or neither?

To determine the relationship between the lines represented by the equations \(y = 4x + 2\) and \(y = 4x - 7\), we need to analyze their slopes. The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. 1. For the first equation \(y = 4x + 2\): - The slope \(m_1\) is \(4\). 2. For the second equation \(y = 4x - 7\): - The slope \(m_2\) is also \(4\). Since both lines have the same slope (\(m_1 = m_2 = 4\)), they are parallel. Thus, the lines represented by the equations \(y = 4x + 2\) and \(y = 4x - 7\) are **parallel**.