Question

How do I corporate the fraction (in the ones with fractions) (3,11)

Example: y=2/3x + 4
11=2/3(3) + 4

Answer 1

The matched equation and coordinate pairs:

a) y=2x+5 = (3,11),

b)
`y=(2)/(3)x+4` = (-6,0),

c) y=-3x+7 = (4,-5) and

d)
`y=(1)/(5)x-2` = (5,-1).

Explanation:

We are given with coordinate pairs and its equation. Check that applying the x value in the coordinate pair gives the answer y.

Let us match the coordinate points by applying into each equations.

a) y=2x+5.

Substitute (5,-1)

-1=2(5)+5.

-1≠15.

Substitute(4, -5)

-5=2(4)+5.

-5≠13.

Substitute(3,11)

11=2(3)+5.

11=11.

∴(3,11) is the coordinate pair for y=2x+5.

b)
`y=(2)/(3) x+4`.

Substitute (5,-1)

`-1=(2)/(3)(5)+4`.

`-1=(10)/(3) +4.`

The denominator should be same in order to continue further. 4 has no denominator it means the denominator is 1. it can be represented as
`(4)/(1)`.

Multiply 3 on both numerator and denominator in
`(4)/(1)`.

`-1=(10)/(3) +(4)/(3)`.

`-1=(10+12)/(3)`.

-1×3=22.

-3≠22.

Substitute (4,-5)

`-5=(2)/(3)(4)+4.`

`-5=(20)/(3)`.

-15≠20.

Substitute(-6,0)

`0=(2)/(3) (-6)+4.`

0=-12+12.

0=0.

∴(-6,0) is the coordinate pair for
`y=(2)/(3)x+4.`

c) y=-3x+7.

substitute(5,-1)

-1=(-3)5+7.

-1= -15+7.

-1≠ -8.

Substitute(4, -5)

-5= (-3)(4)+7.

-5= -12+7.

-5= -5.

∴(4,-5) is the coordinate pair for y=-3x+7.

⇒(5,-1) is the coordinate pair for
`y=(1)/(5)x-2`.