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
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-2=\dfrac{5-2}{4-2}(x-2)[/tex]
[tex]y-2=\dfrac{3}{2}(x-2)[/tex]
[tex]y-2=\dfrac{3}{2}(x)+\dfrac{3}{2}(-2)[/tex]
On further simplification, we get
[tex]y-2=\dfrac{3}{2}(x)-3[/tex]
[tex]y=\dfrac{3}{2}(x)-3+2[/tex]
[tex]y=\dfrac{3}{2}(x)-1[/tex]
Therefore, the correct option is A.
