The Introduction of Graphing

If you would like, you can learn about graphs themselves first by clicking here.

        Graphing can be complicated due to the many different aspects there are to graphing. In order to graph something, you need to have the equation that you want to graph. At first, generally, you would only do graphs of equation that are of power 1, meaning that all the variables (which there should only be two variables, X and Y) are only raised to the first power. The equation for you to graph can be given in many forms.

        The easiest form to graph from would be the slope-intercept form (Y=mX+b). This is because the first point you can put on the graph is (0,b) because b represents the point where the line intercepts the Y axis. After you have that point, you can start putting in X values on either side of 0, such as -2,-1,1,2 and plot those points. These three forms of equations are for equations that are to a single power, meaning that both X and Y are only raised to the first power. Eventually, you get to the point where either X, Y or both of them are raised to powers that are not 1. An example would be in the equation Y=X², where X is being raised to the second power. To graph this you could still try to graph it the same way, start at where X=0 and find out the Y coordinate, plot the point, then try points where X=-2,-1,1,2 until you get a good idea of what it looks like.

****Slopes****

        If you are trying to find out the equation of a line if you only have 2 points, you can do so by using slope. To find the slope of the line that would be formed by connecting the two points is found by using the formula slope=(rise)/(run). Rise in this case means how much the Y coordinate increased from point1 to point2. Run is how far it went along the X-axis, or in easier terms how much the X coordinate increased from point1 to point2. To find out how it much it increased, the X coordinate and/or the Y coordinate, simply subtract the X(or Y, whatever the case may be) coordinate of the first point from the X(or Y) coordinate of the second point.

        The next easiest way to try to graph a line is by using its slope. In order to do this you already need to have a point on the graph, or know where it intercepts the Y-axis.

        These equations where Y is equal to some thing that involves X are called functions. The usual notation for a function is f(X). Y=X² is considered a function. So is Y=mX+b. They are both considered to be functions of X. They would be written as f(X)=X² and f(X)=mX+b, respectively.

To continue onto a more detailed look at binomials and functions, click next.

To go back to the introduction of graphs, click here.