Question

How do you graph `2x + y = 3` by plotting points?

Answer 1

Find a few `(x,y)` pairs that satisfy the equation; plot these points; connect them.

Explanation:

Pick some values for `x`, and use the equation to find what `y` must be for each of those `x`'s.

For example, if `x` is 0, then we have:

`"         "2x+y=3`
`=>2(0)+y=3`
`=>"     "0+y=3`
`=>"            "y=3`

So when `x=0`, we have `y=3`. Meaning the point `(x,y)=(0,3)` is a solution to `2x+y=3`, and so our graph of the equation will pass through `(0,3)`.

We can get a few more points:

If `x=1`, then

`"         "2x+y=3`
`=>2(1)+y=3`
`=>"     "2+y=3`
`=>"            "y=1`

So `(x,y)=(1,1)` is also on our graph.

Similarly, if `x=2`, then we get `y="–"1`, giving us the point `(x,y)=(2,"–"1)`.

We then take the points we've computed, `(0,3), (1,1), (2,"–"1)`, and plot them on a graph:

graph{((x)^2+(y-3)^2-.02)((x-1)^2+(y-1)^2-.02)((x-2)^2+(y+1)^2-.02)=0 [-10, 10, -5, 5]}

Last, since we know this equation is linear, we just need to connect the dots with a line:

graph{((x)^2+(y-3)^2-.02)((x-1)^2+(y-1)^2-.02)((x-2)^2+(y+1)^2-.02)(2x+y-3)=0 [-10, 10, -5, 5]}

And we're done!