Question

For the equation '`y= 1/3 x`, what are the given pairs `(-3,y_1 ) (0,y_2 ) (x_1 ,3)` ?

Answer 1

`(-3,color(white)("d")y_1)=(-3,-1)`
`(color(white)("ddd")0,color(white)(".")y_2) =(color(white)("ddd")0,color(white)(".d")0 )`
`(color(white)("d.d")x_1,color(white)("d")3)=(color(white)("ddd")9,color(white)(".d")3)`

Explanation:

Given relationship: `color(green)(y=1/3x" "...Equation(1)`

We will also need `x="something"` so lets deal with that

Multiply both sides by `color(red)(3)`. This will turn the `1/3` from `1/3x` into 1. I am doing this because `1xx x =x`

`color(green)(y=1/3xx x color(white)("dddd")->color(white)("dddd")ycolor(red)(xx3)color(white)("d")=color(white)("d")1/3color(red)(xx3)xx x)`

`color(green)(color(white)("dddddddddddd.")->color(white)("dddddd")3y color(white)("d")= color(white)("d")color(red)(3)/3xx x`

`color(green)(color(white)("dddddddddddd.")->color(white)("dddddd.")3ycolor(white)("d")=color(white)("d")x" ".....Equation(2)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider the pair "(x,y)->(color(red)(-3),y_1))`

Need to determine `y_1` so using `Eqn(1)`

`color(green)(y=1/3x color(white)("ddd")->color(white)("ddd")y= 1/3xx color(red)((-3)))`

`color(green)( color(white)("ddddddddd")->color(white)("ddd")y=-1)`

`color(white)("dddddd")color(blue)( (-3,y_1)->(-3,-1) )`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider the pair "(x,y)->(color(red)(0),y_2))`

Need to determine `y_2` so using `Eqn(1)`

`color(green)(y=1/3x color(white)("ddd")->color(white)("ddd")y= 1/3xx color(red)((0)))`

`color(green)( color(white)("ddddddddd")->color(white)("ddd")y=0)`

`color(white)("dddddd")color(blue)( (0,y_2)->(0,0 ) )`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider the pair "(x,y)->(x_1,color(red)(3),))`

Need to determine `x_1` so using `Eqn(2)`

`color(green)(3y=x_1 color(white)("ddd")->color(white)("ddd")3xxcolor(red)(3)= x_1)`

`color(green)( color(white)("ddddddddd")->color(white)("ddd")x_1=9)`

`color(white)("dddddd")color(blue)( (x_1,3)->(9,3) )`