When first introduced to graphing lines, we often use a table of values to plot points and connect them. There are several other methods of graphing lines, including using a point and the slope. Sometimes graphing lines using an equation involves the same methods as using a table of values. Since we graph lines in the coordinate plane, it is necessary to understand how to connect graphs, tables and equations.
There are different methods you could use to go from an equation to a graph.
Making a table is one of the most fundamental or basic level strategies for graphing a line. And, by the way, making a table will work when you start moving through your high school career and getting into other types of equations like curves. You can make a table for them also.
But let's check it out for lines. When you want to graph a line by making a table, keep in mind any point represents a solution to the equation. And here's what I mean. Every point has an X number and a Y number. When I input an X number into my equation,my Y value's my output. So any point that's on the line is a true solution to that equation. That becomes useful when you're making a table.
Tables usually look like this. You can either make them horizontally or vertically like that, if you want to. Totally up to your preference. And what you do is you choose any X numbers you want to. It's usually a good idea to use some negative values in addition to some positive values. And then what you do is one by one you're going to substitute these X numbers into your equation as inputs to find your corresponding Y value output. Then each one of these is going to turn into a point on your graph and you'll just connect them using a ruler.
One thing I want to make sure I point out to you guys before you start this process is that you want your points to be ruler-straight. Here's what I mean.
Let's say I get my points on there and they kind of look like this and I have one that's kind of like out there. Well, these three are straight. So that's probably what the line looks like. But this point, I probably made an error. If I got three that are perfectly lined up, they're ruler-straight and I used a ruler to draw them and I have this point, that's just like a little bit off, chances are I made an error in my table. So go back to your table and make corrections.
Most people tend to do at least three points in their table to start with. I would recommend for your first tables you start doing, you start by doing about five points. And, again, you're going to substitute your X numbers in to find your Y values and then put those dots on the graph. They should make a ruler-straight line.