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Consider the questions below:

Are the line parallel or perpendicular?

Consider the questions below: Are the line parallel or perpendicular?-example-1

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\Large\textsc{Answer\::}

  1. Parallel
  2. Perpendicular


\Large\textsc{\textbf{Calculations\::}}

First , notice that the equation of the second line , 6x=3y+5 , is not written in the same form as y=2x , so determining the slope is hard .

To determine the slope , we need to convert the first equation into slope intercept form .

Subtract 6x on both sides :

0 = 3y+5-6x

Now , subtract 3y on both sides :

-3y=-6x+5

Divide by -3 on both sides :

y=-6/-3x+5/-3

Which simplifies to :

y=2x-5/3 (remember , a negative divided by a negative results in a positive)

Put both equations together :

y=2x and y=2x-5/3

Notice that the slopes are the same . This indicates that the lines are parallel .

Now let's focus on the second maths problem :

Consider the equations below .

x=-4 and y=-2

Are the lines parallel or perpendicular?

The slope of the first line is undefined , and the slope of the second line is zero .

Lines with undefined slopes are vertical , and lines with slopes of zero are horizontal .

Here's something you may have recalled from your Geometry class :

Is a vertical line parallel or perpendicular to a horizontal line ?

The ans is : perpendicular .

Henceforth , the lines x = -4 and y = -2 are perpendicular to each other .


\footnotesize{\texttt{hope helpful~}

User Roman Gruber
by
8.8k points
8 votes
Answer: Parallel
i did this yesterday
User Christian Trimble
by
8.0k points

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