Algebra Equations :: Linear Equations and How to Solve Them

Parts of a Linear Equation

There are three major parts of a linear equation:

y and x--the variables

m--the slope-This is how much a line goes up or down divided by every unit that it goes side to side. Example: if a line goes up 2 and to the right 1, then the slope is 2. If it goes up 3 and to the right 4, then the slope is 3/4. A line that goes up and to the right has a positive slope, a line that goes down and to the right is a negative slope.

b--the y-intercept-The place where the line hits the y-axis (the vertical line)

Form of a Linear Equation

The general form of an equation is:


so if you had a slope of 4, and a y-intercept of 5, then your equation would be y=4x+5

Writing an Equation from a Graph

Lets take the graph to the right.  If you identify where the y-intercept is.  You can see that it is at 1.  Then you count how much it goes up and how much it goes side to side.  You can see that it goes up 2 and to the right 1.  Therefore the slope is 2/1, or 2. Using our form


we can replace the b with 1 and the m with 2.  So our answer is:


Lets take a look at this line.  Again, the first step is to identify the y-intercept.  In this case, it is 2.  Next we need to identify the slope.  If we start at (0,2) and follow the line, the next point you can find is (3,1).  This means that the line went down, or negative, 1 and to the right 3.  This means the slope is -1/3.  So our line is:


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