Question

How do you graph `x+3y=6` using intercepts?

Answer 1

Find the intercepts by setting `x=0` or `y=0` and solving, then draw a line through them...

Explanation:

Given:

`x+3y = 6`

we can find the intercepts by setting `x=0` or `y=0` and solving. This is equivalent to crossing out the term involving `x` or that involving `y`.

In any case, putting `x=0` we have:

`3y = 6`

and hence `y = 6/3=2`

So the intersection with the `y` axis (which has equation `x=0`) is at the point `(0, 2)`

Putting `y=0` we have:

`x = 6`

So the intersection with the `x` axis is at `(6, 0)`

Since there are no terms of degree `> 1`, the given equation describes a line through these two intercepts:

graph{(x+3y-6)(x^2+(y-2)^2-0.02)((x-6)^2+y^2-0.02) = 0 [-7.71, 12.29, -3.8, 6.2]}