Question

(05.02)

Two quantities are related, as shown in the table:




x

y

2 3
4 4
6 5
8 6


Which equation best represents the relationship?
y = 1 over 2 x + 2
y = 1 over 2 x + 1
y = x + 2 y = 2x + 1

Answer 1

first equation y=1/2x +2

x=2 = 1/2(2) +2 =1+2 =3

x=4 = 1/2(4)+2 = 2+2 =4

first equation is the answer

Answer 2

`y=(1)/(2)x+2`

A is correct

Explanation:

Given: Table of x and y

x : 2 4 6 8

y : 3 4 5 6

Using two point find the slope:

(2,3) and (4,4)

`Slope=(4-3)/(4-2)`

`\text{Slope }=(1)/(2)`

Now we find slope using last two point

(6,5) and (8,6)

`\text{Slope }=(6-5)/(8-6)`

`\text{Slope }=(1)/(2)`

Slope is equal. Thus, The given relation is linear.

`y-3=(1)/(2)(x-2)`

`y=(1)/(2)x+2`

Hence, The relation represents a linear equation
`y=(1)/(2)x+2`