Question

Two quantities are related, as shown in the table:

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

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-2=\dfrac{5-2}{4-2}(x-2)$

$y-2=\dfrac{3}{2}(x-2)$

$y-2=\dfrac{3}{2}(x)+\dfrac{3}{2}(-2)$

On further simplification, we get

$y-2=\dfrac{3}{2}(x)-3$

$y=\dfrac{3}{2}(x)-3+2$

$y=\dfrac{3}{2}(x)-1$

Therefore, the correct option is A.