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

1 Answer
Mar 18, 2018

(-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) )