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Proving Relationships of Parallel and Perpendicular Lines

Two lines are parallel if their slopes are identical. For this exercise, we have been given two points on each line, so we have enough information to calculate their slopes using the Slope Formula. Note that when choosing points to substitute for and it doesn't matter which points on the line you choose, since the result will be the same. Let's start with line which passes through and
The slope of line is We will use the same method to identify the slope of line
Line Points Slope Simplified Slope

Now that we've identified the slope of each line, we can see that and do not have the same slope, so they are not parallel.