Value of a for Parallel Lines: - 23 Value of a for Perpendicular Lines: 6
Practice makes perfect
In order to determine the value of a, we need to know the slopes of the equations. We will therefore first isolate the y-variables in both equations so that they will be in slope-intercept form and we will be able to determine their slopes.
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Given Form && Slope-Intercept Form [0.8em]
6y=-2x+4 &⇒ & y= -1/3x+2/3
2y=ax-5 &⇒ & y= a/2x-5/2
As a result, the slope of the first line is - 13 and the slope of the second line is a2. Now that we know the slopes of the lines, we can start with finding the value of a such that the lines are parallel.
Parallel Lines
We learned that nonvertical lines are parallel if and only if they have the same slope.
l_1∥ l_2 ⟺ m_1=m_2
According to the statement above, let's find the value of a.
As a result, the lines will be parallel when the value of a is - 23.
Perpendicular Lines
We also know that nonvertical lines are perpendicular if and only if their slopes are negative reciprocals. In other words, the product of the slopes must be -1.
l_1⊥ l_2 ⟺ m_1 * m_2 = -1
Using the statement above, we can find the value of a.
