The slope of the line c is 3. Now that we have identified the slope of each line, let's see them together at a table.
Line
Slope
a
-1/3
b
3
c
3
As we can see from the table, b and c have the same slope. Therefore, they are parallel.
Perpendicular Lines
We can conclude that the lines with different slopes are not parallel. To determine whether or not they are perpendicular, we calculate the product of their slopes. Any two slopes whose product equals -1 are negative reciprocals and are therefore perpendicular. Let's start with checking lines a and b.
The product of the slopes of lines a and b equals -1, so lines a and b are perpendicular. We will use a similar method to check if lines a and c or b and c are perpendicular.
Lines
Slope 1
Slope 2
Product
a & b
-1/3
3
-1
a & c
-1/3
3
-1
b & c
3
3
9
We have found that line a is perpendicular to lines b and c. Notice that if two lines are parallel, they cannot be perpendicular.
