Question

Consider the line x+5y=6

Answer 1

Answer:

$x + 5y = 6$ is perpendicular to $y = 5x + \frac{6}{5}$ and parallel to $y = -\frac{1}{5}x + 2$

Step-by-step explanation:

First, convert the equation to standard form so that y is isolated.

x + 5y = 6 --> x - 6 = -5y (divide both sides by -5) --> $y = -\frac{1}{5}x + \frac{6}{5}$

A perpendicular line will have a slope that is the opposite reciprocal of the original slope (meaning you flip the numerator and denominator then make it negative).

$-\frac{1}{5}$ is perpendicular to $-(\frac{-5}{1} )$ which simplifies to 5.

A parallel line will have the same slope, but the y-intercept will be different. It can be pretty much any number as long as the original slope is used in the new equation.

$y = -\frac{1}{5}x + \frac{6}{5}$ is parallel to $y = -\frac{1}{5}x + 2$ just like $y = -\frac{1}{5}x - \frac{100}{23}$.