Linear Equations
To find the equation of a line, we must know a point on
the line and the slope of the line.
For example, lets find the equation of the following line:
![](./articles_imgs/6482/linear59.gif)
We must first find the slope:
![](./articles_imgs/6482/linear60.jpg)
Now we use one of the given points, say (3,1).
Using the point-slope equation we get
![](./articles_imgs/6482/linear61.jpg)
However, the book wants the equation written in General
Form or Slope-Intercept form:
To put the equation in Slope-Intercept form (y = mx+b), solve the equation for
y:
![](./articles_imgs/6482/linear62.jpg) |
|
![](./articles_imgs/6482/linear63.gif) |
Distribute |
![](./articles_imgs/6482/linear64.gif) |
Add 1 to both sides |
![](./articles_imgs/6482/linear65.gif) |
Simplify |
To put the equation into General Form (Ax+By = C ) , we
must get rid of the fractions:
![](./articles_imgs/6482/linear66.jpg) |
|
4y−4=3(x−3) |
Multiply both sides by 4 |
4y−4=3x−9 |
Distribute |
3x−4y=5 |
Get in the form Ax+By = C |
|