You’ll be drawing lots of graphs of linear equations in two variables in algebra I. For example, y=2x+1. So, what’s a graph?
The graph of a linear equation in two variables is the set of all points (x,y) that satisfy the equation.
How do you know which points satisfy the equation? There’s only one way to find out. Plug it in! Let’s see if the point (0,0) is on the graph of y=2x+1.
y = 2x+1
0 ? 2(0) + 1
0 ? 0 + 1
0 ? 1
Since 0 doesn’t equal 1, then (0,0) is not on the graph. Now we’re getting somewhere! But we can’t check all the points that way. There’s not enough time to check infinitely many points! We have to find an easier way to draw graphs of these things.
If your graph looks like this, y=2x+1, then it’s in the slope-intercept form (or sometimes called the y-intercept form) and it’s super easy to graph. First, we take the +1 and plot it on the y-intercept.
Then, take the 2, which is the coefficient of x, and write it as 2/1. That’s our slope! Remember, slope is rise over run. To plot the slope, start at the y-intercept (0,1) then rise 2 and run 1. The point you land on is the next point on the graph.
Now you just need to draw a line between the two points!
For more help understanding graphs of linear equations in two variables, check out Brightstorm Algebra.