Graphing Lines using a Table of Values - Concept
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.