Question

How do you find the intercepts and graph `x+y=6` ?

Answer 1

Find intercepts and draw a line through them...

Explanation:

Given:

`x+y=6`

Note that if you set `x=0` (or equivalently cover up the `x` term), then the resulting equation is:

`y=6`

Similarly, if you set `y=0` (or equivalently cover up the `y` term), then the resulting equation is:

`x=6`

So the intercepts of this line with the `y` and `x` axes are `(0, 6)` and `(6, 0)` respectively.

We can now draw the graph by drawing a straight line through these two intercepts...

graph{(x+y-6)((x-6)^2+y^2-0.02)(x^2+(y-6)^2-0.02)=0 [-7.75, 12.25, -1.56, 8.44]}

Answer 2

`"see explanation"`

Explanation:

`"one way is to find the intercepts that is where the "`
`"graph crosses the x and y axes"`

`• " let x = 0, in the equation for y-intercept"`

`• " let y = 0, in the equation for x-intercept"`

`x=0to0+y=6rArry=6larrcolor(red)"y-intercept"`

`y=0tox+0=6rArrx=6larrcolor(red)"x-intercept"`

`"plot "(0,6)" and "(6,0)" and draw a straight line"`
`"through them"`
graph{-x+6 [-20, 20, -10, 10]}