# little question

Discussion in 'Physics & Math' started by qfrontier, Sep 7, 2002.

1. ### qfrontierCaptain Of StarshipRegistered Senior Member

Messages:
114
how do you find the equation of this line;

Slope=3
Y-Intercept=2

Using the Ax+By+C=0 method? and what does Ax, By and C suppose to mean?

Thanks for any help!

3. ### EmfuserRegistered Senior Member

Messages:
90
If you're defining a line on a regular x-y plane, you can make the line equation a function of one variable (x or y).

For slope=3, Y-Intercept=2, the basic equation (y=mx + b) is merely a reduction of your equation with the assumption that B=1. Thus Ax + By + C = 0 becomes -3x +y -2 = 0 and can be written as y = 3x + 2 . If B != 1, then you end up with y=(3x+2)/B.

That's my educated guess.

5. ### qfrontierCaptain Of StarshipRegistered Senior Member

Messages:
114
is the y=mx+b form the same as Ax+By+C=0 form?

7. ### EmfuserRegistered Senior Member

Messages:
90
It is for all I can see. If you want to define y in terms of x, then you substitute A for m and C for b s.t. y=(Ax + C)/B = (mx + b)/B

The only thing about the generic y = mx + b equation that excludes the B term is an assumption that B is one or has already been divided into A & C.

8. ### HallsofIvyRegistered Senior Member

Messages:
307
Actually, there is an important difference between "Ax+ By+ C=0" form and "y= mx+ b". The second form cannot be used to represent a vertical line (x= 2 for example) while the first can. (It would be x-2= 0 with A= 1, B=0, C= -2.

9. ### James RJust this guy, you know?Staff Member

Messages:
37,110
qfrontier,

You problem is to relate the undermined coefficients A, B and C to the slope and intercept.

Let's look at the equation:

Ax + By + C = 0

The y intercept is where x=0, so

By<sub>intercept</sub> + C = 0 --- (1)

The slope we get from rearranging the equation:

By = -Ax - C

y = -(A/B)x - (C/B)

This is in the form y = mx + c, where

m = -(A/B) and c = -(C/B)

m is the slope, and c is the y intercept. Notice that if we rearrange equation (1) we get y<sub>intercept</sub> = -C/B, which agrees with this.

You are given that

Slope=3
Y-Intercept=2

so

-C/B = 2
-A/B = 3

We have two equations and three variables, so we can set one of the variables arbitrarily. Let's choose B=1 for simplicity. Then:

C = -2 and A = -3

The equation you want is:

-3x + y - 2 = 0

or y = 3x + 2