are these lines perpendicular, parallel, the same, or neither

(1.) y =2/3 x + 3 and y = -3x + 2

(2.) 2x + 5y = 1 and y = 5/2x +4

- Sep 18th 2009, 08:46 PMtyonnaI need help with these 2 problems i just can't figure out for the life of me
are these lines perpendicular, parallel, the same, or neither

(1.) y =2/3 x + 3 and y = -3x + 2

(2.) 2x + 5y = 1 and y = 5/2x +4 - Sep 18th 2009, 09:30 PMred_dog
Let $\displaystyle d_1:y=m_1x+n_1$ and $\displaystyle d_2:y=m_2x+n_2$.

$\displaystyle d_1\parallel d_2\Leftrightarrow m_1=m_2, \ n_1\neq n_2$

$\displaystyle d_1\perp d_2\Leftrightarrow m_1\cdot m_2=-1$

$\displaystyle d_1=d_2\Leftrightarrow m_1=m_2, \ n_1=n_2$ - Sep 18th 2009, 09:31 PMRapha
Hello tyonna!

You have to check some criteria

Let two lines given by

y1 = ax+b

y2 = cx+d

they are perpendicular, if a*c = -1

they are parallel, if a=c (and b is not equal to d)

Now back to your excersice

(1)y =2/3 x + 3 and y = -3x + 2

It is a = 2/3 and c = -3. It is obvious that these lines are not parallel

EDIT:

But it is a*c = 2/3 * (-3) = -2

This is not equal to -1, because $\displaystyle -2 \not= -1 $

So they are not perp.

Number 2

2x + 5y = 1 and y = 5/2x +4

Solve the first "line" for y

2x + 5y = 1

5y = 1-2x

y =1/5 * (1-2x) = 1/5 - 2/5x = -2/5x+1/5

Okay, and the other line is defined by y = 5/2x +4

It is a = -2/5 and c = +5/2 => they are not parallel, but perpendicular.

Yours

Rapha - Sep 18th 2009, 09:35 PMtyonna
- Sep 18th 2009, 09:38 PMRapha
These are the criteria I mentioned

Two lines are given by

They are parallel, if

They are perpendicular/orthogonal, if

and they are the same/identical, if

- Sep 18th 2009, 09:38 PMtyonna
- Sep 18th 2009, 09:41 PMRapha
- Sep 18th 2009, 09:56 PMtyonna
- Sep 18th 2009, 10:01 PMRapha
They can't be the same, because $\displaystyle a \not= c$.

They are the same, if

a) the lines are parallel, that means a=c, e. g. $\displaystyle m_1 = m_2$

AND

b) b = d, e. g. in red_dog 's post the criteria is $\displaystyle n_1 = n_2$

'Neither' is the right answer for (1)

I'm really sorry for that (Crying)

I'm glad you didn't go offline and checked the forum again. - Sep 18th 2009, 10:05 PMtyonna