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

1 Answer
Aug 1, 2015

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.