Write an equation parallel and perpendicular to y=5x+2

Question

I have no idea how to do this. I am completely lost. It would be amazing if someone could help me right now.

Answer 1

Write an equation parallel and perpendicular to y = 5x + 2

SOLUTION:

There are an infinite number of lines, that are parallel to the given line.

Any line that has the same slope will be parallel to the given line.

The given line has a slope of 5.

So, any line with a slope of 5 will be parallel to the given line.

Here are a some:

y = 5x + 5

y = 5x + 4

y = 5x + 3

y = 5x = 1

y = 5x

y = 5x - 1

y = 5x - 2

In general: y = 5x + b

...

There are an infinite number of lines, that are perpendicular to the given line.

Any line that has a slope that is the negative reciprocal

of the slope of the given line, will be perpendicular to it.

The given line has a slope of 5. So, any line with a slope of -1/5

will be perpendicular to the given line. Here are a some:

y = (-1/5)x + 3

y = (-1/5)x + 2

y = (-1/5)x + 1

y = (-1/5)x

y = (-1/5)x - 1

y = (-1/5)x - 2

In general; y = (-1/5)x + b

Answer 2

First, what is the slope of this line? It's in y = mx + b form and m is the slope. So the slope is 5.

A parallel line will have the same slope so some examples would be:

y = 5x + 7

y = 5x - 3

y = 5x

A perpendicular line will have a slope that it is the negative reciprocal of the original slope ( flip it and change the sign). So the slope will be - 1/5. Some examples are:

y = -1/5x + 4

y = -1/5x - 2

y = -1/5x