Finding a linear equation is actually about graphing the linear function using $y=mx+b$ or $y=mx$.

We can find the linear equation in $5$ ways:

- Using a point on the line and the slope of the line.
- Using two points that lie on the line.
- Using the graph of the function itself.
- Using parallel lines, that is, if the requested line is parallel to another line and we know the slope of the other line.
- Using perpendicular lines, that is, if the requested line is perpendicular to another line and we know the slope of the other line.

**The first three methods are based in one way or another on the general formula for finding the linear equation:**

$y-y1=m\times\left(x-x1\right)$

The last two methods also use this formula, but they also take into account two additional rules:

- For parallel lines, the slopes are equal, that is $m1=m2$
- For perpendicular lines, the slopes have the relationship $m1\times m2=-1$