For this exercise, we have been given the equation of each line, so we will rewrite each of them in slope-intercept form to identify their slopes. Let's start with line a.
In the same way, we can write lines b and c in slope-intercept form.
Line
Given Equation
Slope-Intercept Form
Slope
a
2x-7y=14
y=2/7x-2
2/7
b
y=7/2x-8
y=7/2x-8
7/2
c
2x+7y=-21
y=-2/7x-3
-2/7
Now that we have identified the slope of each line, we can see that none of the lines have the same slope. Therefore, none of the lines are parallel.
Are They Perpendicular?
For lines with different slopes, we can conclude that they are not parallel. To determine whether or not they are perpendicular, we will calculate the product of their slopes. Any two slopes whose product equals -1 are negative reciprocals, and are therefore perpendicular. Let's start by checking lines a and b.
