## How to Find The Equation of a Line

So you want to know how to find the equation of a line.  This is a skill you must know as an algebra student.  Before I explain the steps to find the equation of a line I like to stress that we like to write all linear equations (line equations) in the form y=mx + b.  Now it’s not required to write an equation of a line in the y=mx + b form but it’s the most common way we see lines written in algebra.  Ok with that said lets get into finding the equation of a line.  To find the equation of a line you will need the slope (m) and at least one point (x, y) that is on the line.  For example if we know a line has a slope = 3 and passes through the point (1, 7) we can easily find the y=mx + b equation of this line- I will explain how in a bit.  Now sometimes we are asked to find the equation of a line given two points that are on the line- i.e. no slope information.

Well don’t panic we can still find the equation. What we have to do is use the two points to calculate the slope (m) and then use either one of the given points to find y=mx + b.  Now for the good part, finding the equation of a line given the slope and a point is easy.  From my experience the easiest way to find the equation of a line is to use the point slope formula- I explain in the notes below.  As long as you have the slope and a point and plug in the information correctly into the formula you will obtain the right line equation every time.  For the record “line equations- y=mx + b” should be referred to as “linear equations”…I just think line equation is more descriptive but whatever…lol.  Ok, study hard this is important stuff to know as an algebra student.

some key topics that involve finding the equation of a line:

* point-slope formula
* slope-intercept formula
* slope
* linear models
* best fitting lines and scatter plots