Determining Parallel and perpendicular

Question

2x-4y=91/3x=2/3y-8

Answer 1

Hello, Gregory

 

What you wrote is kind of difficult to understand...

 

But, let me tell you the rules.  Let us use 2x-4y=91 and you want to find a line that is parallel to 2x-4y=91.  Here are the steps:

a) find the slope of 2x-4y=91.  You can do that by rewriting the equation in the slope-intercept form.  y=mx+b. In this case,

 

2x-4y=91

-2x       -2x

-4y=-2x+91    Divide both sides by -4

y=(1/2)x-(91/4)

 

So, the slope of 2x-4y=91 is m=1/2... Any line that has an slope of 1/2 will be parallel to 2x-4y=91 (as long as it has a different y intercept)...

 

Now, if you want to find a line that is perpendicular to 2x-4y=91, you must find the NEGATIVE RECIPROCAL of its slope.  Since the slope of 2x-4y=91 is 1/2, the negative reciprocal will be -2/1 0r just -2.  So, any line that has a slope of -2, it is perpendicular to 2x-4y=91.

 

Real quick... I know that a lot of students don't get the concept of NEGATIVE RECIPROCAL.. Negative means that the sign will become the opposite and reciprocal means turn the slope up-side down: Here are some examples

 

a)7.... change the sign  -7..... turn upside down 1/(-7)

b) -2/3...... change the sign  2/3..... turn upside down 3/2

c) -1....... change the sign  1..... turn upside down 1/1 becomes 1/1.. or just 1

d) -9.........change the sign  9...... turn up side down 1/9

e) 1/5 ..... change the sign -(1/5).... turn upside down -5/1  or just -5

 

I hope this helps a little... please don't forget to rate my answer. Take care...

D. Y. T.