Graphing Lines
Graphing lines is one of the easiest topics in algebra because the process is so straight-forward, as long as you understand a few important things:
1. You must always get the equation into the slope-intercept form before you graph it.
2. You have to know that slope is rise over run.
3. Starting at the y-intercept is the easiest way to do it.
So say we want to graph the equation y = (4/3)x + 2. We know that the line is going to cross the y-axis at 2, so go ahead and put a dot there at (0, 2).
Now from the point at (0, 2), go to the right 3 units, and up 4 units. Now place another dot. Draw a line through the two dots, and you have just graphed the line. It should look like this graph:
If the slope was -4/3 instead, then you would go to the right 3 units, and down 4 units instead. Remember that lines with a positive slope go /, while lines with a negative slope go \.
So how do you graph y = 2? You draw a horizontal line that crosses the y-axis at 2.
How do you graph x = -3? You draw a vertical line that crosses the x-axis at -3.
All you have to do to graph a line when you’re given an equation is to put it in slope-intercept form, note what the slope and y-intercept are, and then use that information to quickly draw the graph. Start with one point at the y-intercept, then use what you know about the slope and rise over run to find a second point, starting at the first point you already have at the y-intercept. Then connect the two lines, and you’re done. It’s that easy.
You should double check to make sure that you counted the right number of spaces when finding the second dot, and that you have made the line / or \ according to whether the line has a positive slope or a negative slope, respectively.