Answered

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Consider the line x+5y=6
What is the slope of a line perpendicular to this line?

What is the slope of a line parallel to this line?

Sagot :

mlm2310

Answer:

[tex]x + 5y = 6[/tex] is perpendicular to [tex]y = 5x + \frac{6}{5}[/tex] and parallel to [tex]y = -\frac{1}{5}x + 2\\[/tex]

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) --> [tex]y = -\frac{1}{5}x + \frac{6}{5}[/tex]

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).

[tex]-\frac{1}{5}[/tex] is perpendicular to [tex]-(\frac{-5}{1} )[/tex] 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.

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

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