# determine if the two lines are parallel, perpendicular, or neither. x-5y=2 and 5x-y=2?

Relevance
• x-5y = 2, 5x – y = 2

x-5y = 2 → 5x – y + k = 0 ….. perpendicular5x-y = 2 → x-5y + k = 0 is perpendicularSo given equation is perpendicular.

• :-

Line 1

5y = x - 2

y = (1/5) x - 2/5

Line 2

y = 5x - 2

Neither perpendicular or parallel

• x - 5y = 2 and 5x - y = 2 are neither

parallel nor perpendicular.

• ax+by=c and kax+kby=d are parallel for non-zero k.

ax+by=c and kbx-kay=d are perpendicular for non-zero k.

These equations don't match either pattern, so neither.

• express the equations in the slope intercept form ("y = mx + c" where m is the slope and c is the y-intercept), and look at the two different values of m. If they are equal, then the lines are parallel or the same. If one "m" equals the negative reciprocal of the other, then they are perpendicular to each other. otherwise the answer's "neither"

• Solve both equations for y to see the slopes of each equation.  Then we can tell if they are parallel, perpendicular, or neither:

x - 5y = 2 and 5x - y = 2

-5y = -x + 2 and -y = -5x + 2

y = (1/5)x - 2/5 and y = 5x - 2

In order for them to be parallel, the slopes would have to be the same.  They are different so this isn't the answer.

In order for them to be perpendicular, the slopes would have to be opposite-reciprocals (aka, the product of the two is -1).  They are only reciprocals, so this isn't the answer.

So they are neither parallel nor perpendicular.