Question

(04.07A)

Two quantities are related, as shown in the table below:


x y
2 3
4 4
6 5
8 6


Which equation best represents the relationship?

Answer 1

y = -1/2x + 11

Answer 2

The equation that best represents the relationship is
`y=(1)/(2)x+2`.

Explanation:

We are given the following table representing the two quantities below;

x y

2 3

4 4

6 5

8 6

Firstly, we will find the two-point slope here, that is;

Consider two points; (
`x_1,y_1`) = (2, 3) and (
`x_2,y_2`) = (4,4)

Now, the formula for finding slope is;

Slope =
`(y_2-y_1)/(x_2-x_1)`

=
`(4-3)/(4-2)` =
`(1)/(2)`

Similarly, finding the slope for the points (6,5) and (8,6);

Slope =
`(y_2-y_1)/(x_2-x_1)`

=
`(6-5)/(8-6)` =
`(1)/(2)`

Now, the linear equation of the line having slope is given by;

`y-y_1=m* (x-x_1)` ; where m = slope and consider (
`x_1,y_1`) = (2, 3)

So, the equation of the line is;

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

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

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

Hence, the equation that best represents the relationship is
`y=(1)/(2)x+2`.