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

Apr 10, 2018

By converting it into slope-intercept form and then inputting x's to get y's.

#### Explanation:

The easiest way to solve this is to convert it into slope-intercept form, which is $y = m x + b$.

You subtract $- 4 x$ on both sides to get

$- 3 y = - 4 x - 6$.

Then you divide $- 3$ on both sides to isolate y, and you are left with

$y = 4 / 3 x - 2$.

Then, you would input x-inputs to get y-inputs for your points.

So if your x-input is 2, then you would do this

$y = 4 / 3 \left(2\right) - 2$ or just $y = 2 / 3$.

Apr 10, 2018

#### Explanation:

$\text{ }$
Given:

The Linear Equation: color(red)(4x-3y=6

Note that this is the equation of a straight line.

The most common form of the equation is color(blue)(y=mx+b, where

color(blue)(m is the Slope or the Gradient, and

color(blue)(b is the y-intercept.

This form is referred to as the Slope-Intercept Form.

color(green)("Step 1"

Reduce color(red)(4x-3y=6 to the Slope-Intercept Form.

$4 x - 3 y = 6$

Get color(blue)(y on one side of the equation and the rest on the other side.

Subtract $4 x$ from both sides.

$\Rightarrow 4 x - 3 y - 4 x = 6 - 4 x$

$\Rightarrow \cancel{4 x} - 3 y - \cancel{4 x} = 6 - 4 x$

Rearrange the terms as

$\Rightarrow - 3 y = - 4 x + 6$

Rewrite pulling $\left(- 1\right)$ out from both sides:

$\Rightarrow - 1 \left(3 y\right) = - 1 \left(4 x - 6\right)$

Divide both sides by $\left(- 1\right)$ to simplify.

$\Rightarrow \frac{\left(- 1\right) \left(3 y\right)}{- 1} = \frac{\left(- 1\right) \left(4 x - 6\right)}{- 1}$

$\Rightarrow \frac{\cancel{- 1} \left(3 y\right)}{\cancel{- 1}} = \frac{\cancel{- 1} \left(4 x - 6\right)}{\cancel{- 1}}$

$\Rightarrow 3 y = 4 x - 6$

Keep color(blue)(y on the left-hand side and move color(blue)(3 to the right-hand side of the equation.

Divide both the sides of the equation by $\textcolor{b l u e}{3}$.

$\Rightarrow \left(\frac{1}{3}\right) \left(3 y\right) = \left(\frac{1}{3}\right) \left(4 x - 6\right)$

$\Rightarrow \left(\frac{1}{\cancel{3}}\right) \left(\cancel{3} y\right) = \left(\frac{1}{3}\right) \left(4 x - 6\right)$

Distribute $\left(\frac{1}{3}\right)$ into the expression.

$\Rightarrow y = \left(\frac{1}{3}\right) \left(4 x\right) - \left(\frac{1}{3}\right) \left(6\right)$

rArr y = (1/3)(4x)-(1/cancel 3)(cancel 6^color(red)2))

$\Rightarrow y = \left(\frac{4}{3}\right) x - 2$

Observe that color(blue)(y = (4/3)x-2 is in the Slope-Intercept Form.

where

color(blue)(m=(4/3) is the Slope or the Gradient, and

color(blue)(b=(-2) is the y-intercept.

For this equation generate a table with $x$ and $y$ values:

Using this table of values, create a graph as shown below:

Hope it helps.