Question

How do you create a table of values to graph `2x-6y=12`?

Answer 1

Please see below.

Explanation:

It is a linear equation, so it may be appropriate and sufficient to the graphselect three points wide apart to draw the graph.

Let `x=0`, then we have `0-6y=12` or `y=12/(-6)=-2` and hence our first point is `A(0,-2)`.

Next let `y=0`, then we have `2x-0=12` or `x=12/2=6` and hence our second point is `B(6,0)`.

Let us select another point with `x=-6`, then we have `2xx(-6)-6y=12` or `-12-6y=12` or `6y=-24` or `y=24/(-6)=-4` and our tird point is `C(-6,-4)`.

Table could be

Table`color(white)(XXXXX)xcolor(white)(XXXXX)y`

A`color(white)(XXXXXXX)0color(white)(XXXX)-2`

B`color(white)(XXXXXXX)6color(white)(XXXXX)0`

A`color(white)(XXXXXX)-6color(white)(XXXX)-4`

Now just join points to get the graph, which appears as below.
graph{2x-6y=12 [-9.75, 10.25, -7.44, 2.56]}