# How do you graph 6x-4y=16?

Aug 31, 2017

See a solution process below:

#### Explanation:

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

First Point:

For $x = 0$

$\left(6 \cdot 0\right) - 4 y = 16$

$0 - 4 y = 16$

$- 4 y = 16$

$\frac{- 4 y}{\textcolor{red}{- 4}} = \frac{16}{\textcolor{red}{- 4}}$

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

Second Point:

For $x = 2$

$\left(6 \cdot 2\right) - 4 y = 16$

$12 - 4 y = 16$

$- \textcolor{red}{12} + 12 - 4 y = - \textcolor{red}{12} + 16$

$0 - 4 y = 4$

$- 4 y = 4$

$\frac{- 4 y}{\textcolor{red}{- 4}} = \frac{4}{\textcolor{red}{- 4}}$

$y = - 1$ or $\left(2 , - 1\right)$

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

graph{(x^2+(y+4)^2-0.08)((x-2)^2+(y+1)^2-0.08)=0 [-20, 20, -10, 10]}

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

graph{(6x-4y-16)(x^2+(y+4)^2-0.08)((x-2)^2+(y+1)^2-0.08)=0 [-20, 20, -10, 10]}