Ross Ward
07/14/2023 · Junior High School
Are the lines represented by the equations \(y = 0.5x + 2\) and \(y = 0.5x - 3\) parallel, perpendicular, or neither?
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Step-by-step Solution
To determine the relationship between the lines represented by the equations \(y = 0.5x + 2\) and \(y = 0.5x - 3\), we need to examine their slopes.
The general form of a linear equation is \(y = mx + b\), where \(m\) represents the slope of the line.
1. For the first equation \(y = 0.5x + 2\), the slope \(m_1\) is \(0.5\).
2. For the second equation \(y = 0.5x - 3\), the slope \(m_2\) is also \(0.5\).
Since both lines have the same slope (\(m_1 = m_2 = 0.5\)), we can conclude that the lines are parallel.
Thus, the lines represented by the equations \(y = 0.5x + 2\) and \(y = 0.5x - 3\) are **parallel**.
Quick Answer
The lines are parallel.
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