Very simple proof!

[Jaskaran]

Hi all, I've been doing some practise problems and one of them is asking me to prove something. This is very basic algebra, but I'm stuck!

Let y = m[sub:1xnwrxfb]1[/sub:1xnwrxfb]x +b[sub:1xnwrxfb]1[/sub:1xnwrxfb] and y = m[sub:1xnwrxfb]2[/sub:1xnwrxfb]x + b[sub:1xnwrxfb]2[/sub:1xnwrxfb]

"If m[sub:1xnwrxfb]2[/sub:1xnwrxfb] = m[sub:1xnwrxfb]1[/sub:1xnwrxfb], then the two lines are parallel."

There's also "If the two lines are parallel, then m[sub:1xnwrxfb]2[/sub:1xnwrxfb] = m[sub:1xnwrxfb]1[/sub:1xnwrxfb]"

What exactly is the difference and how do I prove this?

The other two problems ask me to proove that "if m[sub:1xnwrxfb]2[/sub:1xnwrxfb] = -1/m[sub:1xnwrxfb]1[/sub:1xnwrxfb], then the two lines are perpendicular" and worded the other way around, for the second part.

-Jaskaran.

 

[Deleted member 4993]

Hi all, I've been doing some practise problems and one of them is asking me to prove something. This is very basic algebra, but I'm stuck!

Let y = m[sub:z15ng3z1]1[/sub:z15ng3z1]x +b[sub:z15ng3z1]1[/sub:z15ng3z1] and y = m[sub:z15ng3z1]2[/sub:z15ng3z1]x + b[sub:z15ng3z1]2[/sub:z15ng3z1]

"If m[sub:z15ng3z1]2[/sub:z15ng3z1] = m[sub:z15ng3z1]1[/sub:z15ng3z1], then the two lines are parallel."

There's also "If the two lines are parallel, then m[sub:z15ng3z1]2[/sub:z15ng3z1] = m[sub:z15ng3z1]1[/sub:z15ng3z1]"

What exactly is the difference and how do I prove this?

The other two problems ask me to proove that "if m[sub:z15ng3z1]2[/sub:z15ng3z1] = -1/m[sub:z15ng3z1]1[/sub:z15ng3z1], then the two lines are perpendicular" and worded the other way around, for the second part.

-Jaskaran.

I am at a loss to interpret too - what does the problem actually asking for.

Restated another way - it could mean:

Show that y = mx + b[sub:z15ng3z1]1[/sub:z15ng3z1] and y = mx + b[sub:z15ng3z1]2[/sub:z15ng3z1] do not intersect when b[sub:z15ng3z1]1[/sub:z15ng3z1] & b[sub:z15ng3z1]2[/sub:z15ng3z1] are not equal.


The second one is easier to interpret.

here they are asking you to prove

a) given m[sub:z15ng3z1]1[/sub:z15ng3z1] = -1/m[sub:z15ng3z1]2[/sub:z15ng3z1] -> prove lines are are perpendicular to each other

and

b) given lines are are perpendicular to each other m[sub:z15ng3z1]1[/sub:z15ng3z1] = -1/m[sub:z15ng3z1]2[/sub:z15ng3z1] -> prove m[sub:z15ng3z1]1[/sub:z15ng3z1] = -1/m[sub:z15ng3z1]2[/sub:z15ng3z1]

for a quick review - go to:

http://whyslopes.com/Analytic-Geometry- ... Lines.html


It really depends on the instructor and level of mathematics.