This week in math we learned three types of equations.  General form, Y-intercept form, and point-slope form.  They all tell us something different and some don’t tell us anything at all.

First, let’s start with general form. 0=ax+by+c. We like to call this form the pretty form because it is pretty useless. This form doesn’t tell us anything about our slope, Y-intercept or coordinates.  0=2x-5y+10, this is an example of a general form equation.  To tell this apart from the other equations general form always equals 0 and has to have a positive leading coefficient and can never contain fractions.

The second form is Y-intercept form.  Y=mx+b. This form is the most useful in my opinion when graphing.  This form gives you the slope (rise/run) and it also gives us the Y-intercept, which is our starting point on our graph.  Y= -2x/8 + 5, is an example of Y-intercept form.  The numbers paired with X is always going to be our slope, so in this case, the rise is -2 and our run is 8.  In some cases, you might come across an equation where -2 does not have a visible denominator, all this is saying is that the denominator/run is 1.  The equation is also telling us that our Y-intercept (starting point) is +5.  I know this is Y-intercept form because it has a Y on one side of the equal sign.

Lastly, point-slope form.  m(x-x)=y-y.  To use this form we need to know one point/pair of coordinates and the slope.  2(x-5)=y-3, is an example of the point-slope form.  In this example, 2 (2/1) represents the slope and (5, 3) are the coordinates.  I know this is point-slope form because it has brackets and uses only one pair of coordinates.  This form is the fastest to show an equation of a point on the graph.