Question 648011
Original equations: {{{x-5y=15}}} and {{{5x +y =25}}}

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: {{{y=mx+b}}}

Step 1: Let's start by putting the first equation in slope-intercept form

{{{x-5y=15}}}

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

{{{x-5y=15}}}
{{{-5y=-x+15}}}

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

{{{-5y=-x+15}}}
{{{y=(x/5)-3}}} 

The slope-intercept form of the first line is {{{y=(x/5)-3}}} 

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

{{{5x +y =25}}}
{{{y = -5x + 25}}}

Now, both equations are in slope-intercept form, so let's compare the slopes of both.

The two equations:

{{{y=(x/5)-3}}} <--- The slope of this line is {{{(1/5)}}}
{{{y = -5x + 25}}} <--- The slope of this line is {{{(-5)}}}

The lines have perpendicular slopes because they are opposite reciprocal to each other.

The lines are perpendicular is your answer.