# How do you graph 3y+4x=12?

Feb 15, 2017

This is a straight line through $\left(0 , 4\right)$ and $\left(3 , 0\right)$

#### Explanation:

Notice that the terms are linear or constant, so this equation represents a straight line.

We can find the intersections with the $x$ and $y$ axes by setting $y$ or $x$ equal to zero, or equivalently covering up the corresponding term and solving the resultant equation.

So putting $x = 0$ we get:

$3 y = 12$

Dividing both sides by $3$, we find:

$y = 4$

So the line intercepts the $y$ axis (which has equation $x = 0$) at the point $\left(0 , 4\right)$

If we instead put $y = 0$ then we get:

$4 x = 12$

and hence:

$x = 3$

So the $x$ intercept is at $\left(3 , 0\right)$

We can now draw our line through these two intercepts:
graph{(4x+3y-12)((x-3)^2+y^2-0.01)(x^2+(y-4)^2-0.01) = 0 [-9.21, 10.79, -2.28, 7.72]}