How do you graph 2x+3y=12?

Mar 20, 2018

By rebuilding it to an easier formula.

Explanation:

This formula can be "rebuild" into the regular form of y = a*x + b

We substract 2x from each side of the equation, we then get;

3y = -2x + 12

We then divide everything by 3.

The formula then looks like this;

y = (-2/3 * x) + 12, which you should be able to graph.

Mar 20, 2018

See a solution process below:

Explanation:

First, solve for two points which solve the equation and plot these points:

First Point: For $x = 0$

$\left(2 \cdot 0\right) + 3 y = 12$

$0 + 3 y = 12$

$3 y = 12$

$\frac{3 y}{\textcolor{red}{3}} = \frac{12}{\textcolor{red}{3}}$

$y = 4$ or $\left(0 , 4\right)$

Second Point: For $y = 0$

$2 x + \left(3 \cdot 0\right) = 12$

$2 x + 0 = 12$

$2 x = 12$

$\frac{2 x}{\textcolor{red}{2}} = \frac{12}{\textcolor{red}{2}}$

$x = 6$ or $\left(6 , 0\right)$

We can next plot the two points on the coordinate plane:

graph{(x^2+(y-4)^2-0.035)((x-6)^2+y^2-0.035)=0 [-10, 10, -5, 5]}

Now, we can draw a straight line through the two points to graph the line:

graph{(2x + 3y - 12)(x^2+(y-4)^2-0.035)((x-6)^2+y^2-0.035)=0 [-10, 10, -5, 5]}