Question

Two quantities are related, as shown in the table:

ху
2 2
4 5
68
8 11
Which equation best represents the relationship?
y = 3/2x - 1
y = 3/2x + 2
y = 3/2x
y = 3x + 2

Answer 1

Given:

The table of values.

To find:

The equation that best represents the relationship.

Solution:

From the given table it is clear that the value of x increasing by 2 and the value of y increasing by 3. Since y is increasing at a constant rate with respect to x, therefore the given table represents a linear relationship.

Consider any two points from the given table. Let the two points are (2,2) and (4,5). So, the equation of the line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-2=(5-2)/(4-2)(x-2)`

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

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

On further simplification, we get

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

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

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

Therefore, the correct option is A.