# How do you graph 4x - 3y = 6?

Aug 18, 2017

Find the intercepts with the two axes and draw a line through it.

#### Explanation:

Given:

$4 x - 3 y = 6$

Since this equation contains just linear or constant terms, it describes a straight line.

If we put $x = 0$ or equivalently cover up the term $4 x$, then we get:

$- 3 y = 6$

Dividing both sides by $- 3$, this becomes:

$y = - 2$

So the line passes through $\left(0 , - 2\right)$

If we put $y = 0$ or equivalently cover up the term $- 3 y$, then we get:

$4 x = 6$

Dividing both sides by $4$, this becomes:

$x = \frac{6}{4} = \frac{3}{2}$

So the line passes through $\left(\frac{3}{2} , 0\right)$

Now we can draw our line through these two intercepts:

graph{(4x-3y-6)(x^2+(y+2)^2-0.005)((x-3/2)^2+y^2-0.005)=0 [-5.17, 4.83, -3.42, 1.58]}

Aug 18, 2017

Refer to the explanation for the process.

#### Explanation:

Graph:

$4 x - 3 y = 6$ is the standard form for a linear equation.

We can graph it by solving for the x-intercept $\left(x , 0\right)$ and y-intercept $\left(0 , y\right)$. We only need two points to plot a straight line from a linear equation.

X-Intercept

Set $y = 0$ and solve for $x$.

$4 x - 3 \left(0\right) = 6$

$4 x = 6$

Divide both sides by $4$.

$x = \frac{6}{4}$

Simplify.

$x = \frac{3}{2}$

x-intercept: $\left(\frac{3}{2} , 0\right)$

Y-Intercept

Set $x = 0$ and solve for $y$.

$4 \left(0\right) - 3 y = 6$

$- 3 y = 6$

Divide both sides by $- 3$.

$y = - \frac{6}{3}$

Simplify.

$y = - 2$

y-intercept: $\left(0 , - 2\right)$

Plot the x- and y-intercepts on a grid and draw a straight line between the points.

graph{4x-3y=6 [-10, 10, -5, 5]}