How do you graph -2x-3y=-12 using intercepts?

Aug 17, 2017

See a solution process below:

Explanation:

x-intercept

To find the $x$-intercept set $y$ to $0$ and solve for $x$:

$- 2 x - 3 y = - 12$ becomes:

$- 2 x - \left(3 \times 0\right) = - 12$

$- 2 x - 0 = - 12$

$- 2 x = - 12$

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

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

y-intercept

To find the $y$-intercept set $x$ to $0$ and solve for $y$:

$- 2 x - 3 y = - 12$ becomes:

$\left(- 2 \times 0\right) - 3 y = - 12$

$0 - 3 y = - 12$

$- 3 y = - 12$

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

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

Next, plot these two points.

graph{((x-6)^2+y^2-0.025)(x^2+(y-4)^2-0.025)=0}

Now, draw a line through the two points to graph the line of the equation:

graph{(-2x-3y+12)((x-6)^2+y^2-0.025)(x^2+(y-4)^2-0.025)=0}