Start by identifying the slope and y-intercept of the given equation.
Example Parallel Line: y=3/2x+2 Example Perpendicular Line: y=- 2/3x+4 Explanation: See solution.
Practice makes perfect
To determine whether two lines are parallel or perpendicular, we need to look at their slopes. Let m_1 and m_2 be the slopes of two lines. Let's see the relationship between the slopes in the case where the lines are parallel or perpendicular.
Note parallel lines must have different y-intercepts. Otherwise, both lines are the same. With this in mind, we can write example equations with the desired properties.
Writing the Equation of a Parallel Line
We are given the equation of a line in slope-intercept form. Let's identify the slope and the y-intercept.
Slope-Intercept Form:& y= mx+ b
Given Equation:& y = 32x+( - 1)
To obtain a parallel line, we need the same slope but a different y-intercept. Let's arbitrarily choose a y-intercept of 2. We can now write the equation of a parallel line.
y= 3/2x+ 2
Writing the Equation of a Perpendicular Line
As already explained, perpendicular lines have slopes that are negative reciprocals. Therefore, the product of the slopes is - 1. Let m_1 and m_2 be the slopes of two perpendicular lines.
m_1 * m_2 = - 1
We will substitute 32 for m_1, and solve for m_2.
There is no restriction regarding the y-intercepts of two perpendicular lines. Therefore, let's arbitrarily choose b= 4. We can now write the equation of a perpendicular line.
y= m_2x+ b ⇒
y= - 2/3x+ 4
