# Thread: Simple eqN of a line question

1. ## Simple eqN of a line question

Hey,

I have this question thats been bugging me for a few days now.

$3y-15=2x-8$

Whats the answer if we put it in the eqN of a line?

$2x-3y+7=0$ OR $2x-3y-7=0$?

Thanks for the help.
-NZF

2. Originally Posted by 905
Hey,

I have this question thats been bugging me for a few days now.

$3y-15=2x-8$

Whats the answer (below) if we put it in the eqN of a line?

$2x-3y+7=0$ or $2x-3y-7=0$?

Thanks for the help.
-NZF
are you asking the solution of the line (when y equals 0) or are you asking for us to put the equation in standard/y-intercept/point-slope form?

3. Originally Posted by Quick
are you asking the solution of the line (when y equals 0) or are you asking for us to put the equation in standard/y-intercept/point-slope form?
Put the equation in standard form.

EDIT: Actually it's just part of a question, the only part I don't fully understand.

-NZF

4. Originally Posted by NineZeroFive
Put the equation in standard form.
alright, standard form is in the form of $ax+by=c$ therefore we start with your equation...

$3y-15=2x-8$

add 15 to both sides $3y=2x-8+15$

subtract 2x from both sides: $3y-2x=7$

voila!

~ $Q\!u\!i\!c\!k$

5. Originally Posted by NineZeroFive
Hey,

I have this question thats been bugging me for a few days now.

$3y-15=2x-8$

Whats the answer if we put it in the eqN of a line?

$2x-3y+7=0$ OR $2x-3y-7=0$?

Thanks for the help.
-NZF
Algebraically it would have to be $2x-3y+7=0$. Other standard forms:
$y = \frac{2}{3}x + \frac{7}{3}$ (Slope - Intercept form)

and

$(y - 3) = \frac{2}{3}(x - 1)$ (An example of point-slope form)

and

$\frac{x}{3} - \frac{y}{2} = - \frac{7}{6}$ (I forget what this one is called.)

-Dan

6. Originally Posted by Quick
alright, standard form is in the form of $ax+by=c$ therefore we start with your equation...

$3y-15=2x-8$

add 15 to both sides $3y=2x-8+15$

subtract 2x from both sides: $3y-2x=7$

voila!

~ $Q\!u\!i\!c\!k$
$3y-2x-7=0$? Because it the textbook it says its $2x-3y+7=0$?

7. Originally Posted by NineZeroFive
$3y-2x-7=0$? Because it the textbook it says its $2x-3y+7=0$?

multiply both sides of $3y-2x-7=0$ by negative 1

8. Sorry,

I think I made a typo somewhere.

3y-15=2x-8 is the equation you need to put in the standard form.

Why is it NOT 2x-3y-7=0?

-NZF

9. Originally Posted by NineZeroFive
$3y - 15 = 2x - 8$
$3y - 15 = 2x - 8$

$3y - 15 - 3y = 2x - 8 - 3y$

$-15 = 2x - 3y - 8$

$-15 + 15 = 2x - 3y - 8 + 15$

$0 = 2x - 3y + 7$

-Dan

10. Originally Posted by NineZeroFive
Sorry,

I think I made a typo somewhere.

3y-15=2x-8 is the equation you need to put in the standard form.

Why is it NOT 2x-3y-7=0?

-NZF
I assume you mean:
Originally Posted by NineZeroFive
Sorry,

I think I made a typo somewhere.

3y-15=2x-8 is the equation you need to put in the standard form.

Why is it NOT 3y-2x-7=0?

-NZF
but the answer, both equations are correct, your book is just picky.
although I must say, I've never actually seen standard form equalling zero...

11. Originally Posted by Quick
I assume you mean:

but the answer, both equations are correct, your book is just picky.
although I must say, I've never actually seen standard form equalling zero...
One standard way of writing a multinomial (the "most" standard I've seen, if there is such a thing) is to write the terms of highest degree first down to the lowest degree such that the expression equals zero. For example:
$3x^2y^3 - xy^2 + 12x - 3y + 5 = 0$

In the case for a linear equation the form simply becomes:
$ax + by + c = 0$

I'll admit I don't usually see this form for a line, but considering the expression as a multinomial it would be standard.

-Dan

12. Originally Posted by Quick
I assume you mean:

but the answer, both equations are correct, your book is just picky.
although I must say, I've never actually seen standard form equalling zero...
I'm still kinda confused because the book says "The equation of the line through A and B is 2x-3y+7=0.

Why is it 2x-3y+7=0 and NOT 2x-3y-7=0?

hmm..

-NZF

13. Originally Posted by NineZeroFive
I'm still kinda confused because the book says "The equation of the line through A and B is 2x-3y+7=0.

Why is it 2x-3y+7=0 and NOT 2x-3y-7=0?

hmm..

-NZF
Unless you have a question about my derivation, please see post #9 under this thread. I derived the form there.

-Dan