Question

MATCH EACH EQUATION WITH AN EQUIVALENT EQUATION IN STANDARD FORM

THANKS THIS IS FOR TODAY :(
Have a good day XD

Answer 1

a) standard form of
`y=(2)/(3)x+3` is 2x-3y=-9 Hence Option 3 is correct option.

b) standard form of
`6-y=-5x+8\\` is 5x-y=2 Hence Option 2 is correct option.

c) standard form of
`y-3=4(x-3)\\` is 4x-y=9 Hence Option 4 is correct option.

d) standard form of
`-(7)/(6)x+1=y` is 7x+6y=6 Hence Option 1 is correct option.

Explanation:

The standard form of equation is Ax+By=C

So, we will convert each given question to Ax+By=C and then match the results.

a)
`y=(2)/(3)x+3`

Solving:

`y=(2)/(3)x+3\\y=(2x+9)/(3)\\3y=2x+9\\2x-3y=-9`

So, standard form is 2x-3y=-9 Hence Option 3 is correct option for this question.

b)
`6-y=-5x+8\\`

Solving:

`6-y=5x+8\\5x-y=8-6\\5x-y=2`

So, standard form is 5x-y=2 Hence Option 2 is correct option for this question.

c)
`y-3=4(x-3)\\`

Solving:

`y-3=4(x-3)\\y-3=4x-12\\4x-y=12-3\\4x-y=9`

So, standard form is 4x-y=9 Hence Option 4 is correct option for this question.

d)
`-(7)/(6)x+1=y`

solving

`-(7)/(6)x+1=y \\(-7x+1*6)/(6)=y\\ (-7x+6)/(6)=y\\-7x+6=6y\\Multiplying \ by \ (-1) \ on \ both \ sides:\\7x-6=-6y\\7x+6y=6`

So, standard form is 7x+6y=6 Hence Option 1 is correct option for this question.