# How do you graph y=2/3x-4?

Mar 10, 2018

Refer to the explanation.

#### Explanation:

Graph:

$y = \frac{2}{3} x - 4$ is the slope-intercept form of a linear equation:

$y = m x + b ,$

where:

$m$ is the slope and $b$ is the y-intercept.

You need two points on the line. Let one of the points be the x-intercept and the other point be the y-intercept.

The y-intercept is $- 4$ (from the equation), which is the value of $y$ when $x = 0$. So the point is $\left(0 , - 4\right)$.

The x-intercept is the value of $x$ when $y = 0$.

To determine the x-intercept, substitute $0$ for $y$ and solve for $x$.

$0 = \frac{2}{3} x - 4$

Multiply both sides by $3$.

$3 \times 0 = {\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}^{1} \times \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} ^ 1 x - 4 \times 3$

Simplify.

$0 = 2 x - 12$

Add $12$ to both sides.

$12 = 2 x$

Divide both sides by $2$.

${\textcolor{red}{\cancel{\textcolor{b l a c k}{12}}}}^{6} / {\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}^{1} = \frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}^{1} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} ^ 1$

Simplify.

$6 = x$

$x = 6$

The x-intercept is $\left(6 , 0\right)$.

Plot the x- and y-intercepts and draw a straight line through them.

graph{y=2/3x-4 [-10, 10, -5, 5]}