Question

How do you plot (1,2), (2,5), (3,8), (4,12)?

Answer 1

See the explanation below:

Explanation:

Let's look at the first point `(1,2)`

The first coordinate tells us where to go on the horizontal axis. (usually called the `x` axis when there is no reason to choose some other name).

The point we need has horizontal (`x`) coordinate equal to `1`.
The blue line on this graph show the points whose first coordinate (whose `x` coordinate) is `1`: (We call this blue line a vertical line.)

graph{y = 1000x-1000 [-2.194, 4.742, -1.607, 1.853]}

Note that you can zoom in and out using your mouse wheel, and you can hold and drag the graph around using your mouse.

To plot `(1, 2)` we also need the coordinate on the vertical axis (the `y` coordinate to be `2`.

So we'll add another blue line showing all the points with vertical coordinate equal to `2`:

graph{(y-1000x+1000)(y-2)=0 [-1.54, 4.623, -0.678, 2.398]}

The point `(1, 2)` has to match both descriptions, so it must be on both lines. It is the intersection. I'll put a small circle around the point `(1, 2)`:

graph{(x-1)^2+(y-2)^2 = 1/100 [-1.245, 4.917, -0.432, 2.643]}

Now use the same ideas to locate the point `(2,5)`:
(Remember that you can zoom in and out if you want to.)

graph{(y-1000x+2000)(y-5) = 0 [-8.015, 11.995, -3, 6.984]}

So we want the point

graph{(x-2)^2+(y-5)^2 = 1/81 [-10.05, 18.44, -3.87, 10.34]}

`(3,8)`:

graph{(x-3)^2+(y-8)^2 = 1/81 [-3.74, 21.58, -1.7, 10.93]}

I'll leave the last one for you.