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

Dec 12, 2017

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 $\left(0 , 6\right)$ and $\left(6 , 0\right)$ 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]}

Dec 12, 2017

$\text{see explanation}$

#### Explanation:

$\text{one way is to find the intercepts that is where the }$
$\text{graph crosses the x and y axes}$

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

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

$x = 0 \to 0 + y = 6 \Rightarrow y = 6 \leftarrow \textcolor{red}{\text{y-intercept}}$

$y = 0 \to x + 0 = 6 \Rightarrow x = 6 \leftarrow \textcolor{red}{\text{x-intercept}}$

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