SOLUTION: determine whether the following lines are parallel, perpendicular, or neither: x-5y=15 & 5x +y =25

Question 648011: determine whether the following lines are parallel, perpendicular, or neither:
x-5y=15 & 5x +y =25
Answer by Algebraic(50) (Show Source): You can put this solution on YOUR website!
Original equations: and
To be able to tell whether lines are parallel, perpendicular, or neither, we first have to put them in standard form (slope-intercept form). Then, you must compare both slopes.
If the slopes are the same, the lines are parallel.
If the slopes are opposite reciprocals, the lines are perpendicular.
If there is no resemblance between the slopes, then the lines are neither parallel or perpendicular.
Slope-intercept form:
Step 1: Let's start by putting the first equation in slope-intercept form

We want to get '-5y' by itself so let's subtract 'x' to both sides

Step 2: Now divide '-5' to both sides to get 'y' by itself

The slope-intercept form of the first line is
Let's find the slope-intercept form of the other line
Step 1: Let's start by putting the first equation in slope-intercept form
We want to get 'y' by itself so let's subtract '5x' to both sides

Now, both equations are in slope-intercept form, so let's compare the slopes of both.
The two equations:
<--- The slope of this line is
<--- The slope of this line is
The lines have perpendicular slopes because they are opposite reciprocal to each other.
The lines are perpendicular is your answer.

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