Hi Folks,

Just wondering how one derives the equation of a line y=mx+b from this general expression f(x,y)=a+bx+cy. I believe this expression represents plane geometry.

Any thoughts

Regards

bugatti

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- Mar 29th 2013, 03:42 AMbugatti79Equation of a line derivation
Hi Folks,

Just wondering how one derives the equation of a line y=mx+b from this general expression f(x,y)=a+bx+cy. I believe this expression represents plane geometry.

Any thoughts

Regards

bugatti - Mar 29th 2013, 04:31 AMRuunRe: Equation of a line derivation
Pick one point on the plane, say $\displaystyle (x_{1},y_{1})$ and other one$\displaystyle (x,y)$. We will try to see the relation between $\displaystyle x$ and $\displaystyle y$ Now impose that they are in a line:

Let $\displaystyle \alpha$ be the angle between the black and the red segments. We have $\displaystyle \tan(\alpha)=\frac{\Delta y}{\Delta x}$ where $\displaystyle \Delta y=y-y_1$ and $\displaystyle \Delta x=x-x_1$. Then

$\displaystyle \tan(\alpha)(x-x_1)=(y-y_1) \rightarrow y-y_1=x\tan(\alpha)}-x_{1}\tan (\alpha)$

This is

$\displaystyle \boxed{y=mx+b}$ where $\displaystyle \boxed{m=\tan(\alpha)}$ and $\displaystyle \boxed{b=-x_1 \tan(\alpha)+y_{1}}$ - Mar 29th 2013, 05:16 AMbugatti79Re: Equation of a line derivation
- Mar 29th 2013, 06:13 AMHallsofIvyRe: Equation of a line derivation
f(x,y)= z= ax+ by+ c is the equation of a

**plane**in three dimensions. What do you**mean**by "derive the equation of a line"? Which line? There exist an infinite number of lines in that plane. We could, for example, get the equation of the line where it intersects the xy plane by setting z= 0: 0= ax+ by+ c which is the same as -by= ax+ c and then divide both sides by -b: y= (-a/b)x- (c/b) which is of the form "y= mx+b" with m= -a/b and "b"= -c/b.