Question

How do you graph `5/6x - 6y = 8` by plotting points?

Answer 1

Pick values for `x` and solve for `y`

Only 2 points are needed to graph a line, but additional points can be used to check your answer.

Explanation:

To eliminate the need to deal with fractions, we can multiply all terms of the equation by 6:

`color(red)((6))5/6x-color(red)((6))6y=color(red)((6))8`
`5x-36y=48`

Re-write the equation so that it is in the form `y=...`

`5x-36y=48`
`5x-36ycolor(red)(+36y)color(blue)(-48)=48color(blue)(-48)color(red)(+36y)`
`5x-48=36y`
`(5x-48)/color(red)(36)=(36y)/color(red)(36)`
`y=(5x-48)/36`

Pick values for `x` and calculate the corresponding value for `y`

Let `x=-5`

`y=(5(color(red)(-5))-48)/36 => y=-2.084`

Let `x=0`

`y=(5(color(red)(0))-48)/36 => y=-1.333`

Let `x=5`

`y=(5(color(red)(5))-48)/36 => y=-0.639`

Plot these points and connect with a straight line

graph{5/6x-6y=8 [-10, 10, -5, 5]}