Question

How would you create a `(x,y)` table for the equation `y=2x-1`?

Answer 1

To crate an `(x,y)` table for `y=2x-1`, you could plug in a bunch of `x` values into that equation and find the corresponding `y` values and then tabulate the results. This will give you an idea of what the graph will look like. Note that the graph of `y=2x-1` is a line that goes on forever and ever in the `y` and `x` directions, but by plugging in a few values of choice, you can see a certain part of the graph and then put arrows on the endpoints you get to indicate that the line continues.

So to make a table, you have to pick a few values to plug in. I think that 5 values would be good to start with. Let's say those values are

`x=-4,-2,0,2,4`

Note that you can pick any values you want. I just picked these because they're easy to work with.

So,

`x=-4, y=2(-4)-1=-9`
`x=-2,y=-5`
`x=0, y=2(0)-1=-1`
`x=2, y=2(2)-1=3`
`x=4, y=2(4)-1=7`

You can then tabulate these values with x and y as headings, and whatever inputs you choose under x, and whatever outputs you get under y. It can look something like this:

x -4 -2 0 2 4
y-9 -5 -1 3 7

You can then plot these points to see what the graph will look like. The corresponding points are (-4, -9), (-2,-5), (0,-1), (2,3), and (4,7)
The graph of `y=2x-1` looks like this: