Linear equations are the most basic algebraic equations in Algebra I, and they are also the most basic equations to graph. As indicated by its name, graph of a linear equation is a straight line. It’s important to know that any two points define the position of a straight line. In other words, as long as we can find two points from the equation, we can locate the line in graph.
Example: To graph linear equation Y = 2X + 1.
1). Choose the two easiest points from this equation: (X1, Y1) and (X2, Y2).
The points are: (0, Y1) and (X2, 0).
The point (0, Y1) means that when X=0, then Y=Y1. We choose this point because when X=0, we know that on the graph, this point is surely on y-axis. That is to say, on the y-axis, every point has X = 0.
(Every point on the red line in this graph has X=0.)
The point (X2, 0) means that when Y=0, then X=X2. We choose this point because when Y=0, we know that on the graph, this point is surely on x-axis. That is to say, on the x-axis, every point has y = 0.
(Referring to the graph above, every point on the black line has Y=0.)
2). Solve for these two points. --- Simply plug either X=0 into the equation to solve for Y, or plug Y=0 into the equation to solve for X.
Point (0, Y1) says X=0, so plug it into the equation of Y=2X+1 à Y=2*0 +1 = 1.
So here we’ve solved that Y=1 when X=0. In other words, this point is (0, 1).
Point (X2, 0) says Y=0, so plug it into the equation of Y=2X+1 à 0=2X +1 à X=-0.5
So here we’ve solved that X=-0.5 when Y=0. In other words, this point is (-0.5 , 0).
Now that we’ve found two points for this equation, we can put these points on the graph and simply connect them with a straight line going all the way to both ends. At this point, you’ve done your job nicely!