Is y=-5x+1 and x-5y=30 perpendicular or parallel

Perpendicular lines

Step-by-step explanation:

Parallel lines have the same slope.  In contrast, perpendicular lines have negative reciprocal slopes, in which the product of the slopes of two lines result in -1.

Given the two linear equations, y = -5x + 1 and x - 5y = 30:

Transform x - 5y = 30 into its slope-intercept form, y = mx + b:

x - 5y = 30

x - x - 5y = - x + 30

-5y = -x + 30

Divide both sides by -5:

 (This is the slope-intercept form of the second equation, x - 5y = 30).

Now that we have both equations, it is easier to see that they have negative reciprocal slopes:

y = -5x + 1  ⇒ slope = -5

  ⇒ slope =  1/5

Multiplying their slopes together:  -5 × 1/5 = -1. Therefore, these equations represent perpendicular lines.