Question

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

Answer 1

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=mx+b`.

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

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

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

`y=4//3x-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(2)-2` or just `y=2//3`.

Answer 2

Please read the explanation.

Explanation:

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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.

`4x-3y=6`

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

Subtract `4x` from both sides.

`rArr 4x-3y - 4x=6-4x`

`rArr cancel (4x)-3y - cancel(4x)=6-4x`

Rearrange the terms as

`rArr -3y = -4x+6`

Rewrite pulling `(-1)` out from both sides:

`rArr -1(3y) = -1(4x-6)`

Divide both sides by `(-1)` to simplify.

`rArr ((-1)(3y))/(-1) = ((-1)(4x-6))/(-1)`

`rArr (cancel(-1)(3y))/cancel(-1) = (cancel(-1)(4x-6))/cancel(-1)`

`rArr 3y=4x-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 `color(blue)3`.

`rArr (1/3)(3y)=(1/3)(4x-6)`

`rArr (1/cancel 3)(cancel 3y)=(1/3)(4x-6)`

Distribute `(1/3)` into the expression.

`rArr y = (1/3)(4x)-(1/3)(6)`

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

`rArr y = (4/3)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.