Answer:
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:
[tex]\frac{-5y}{-5} = \frac{-x + 30}{-5}[/tex]
[tex]y = \frac{1}{5}x - 6[/tex] (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
[tex]y = \frac{1}{5}x - 6[/tex] ⇒ slope = 1/5
Multiplying their slopes together: -5 × 1/5 = -1. Therefore, these equations represent perpendicular lines.
