the table given in the question represents relationship B. the function corresponding to relation B is :
y = 15.2 x, where x is the hours worked and y is the amount paid. So y is directly proportional to x.
Now the productivity rate is inversely proportional to the no. of hours worked, i.e as rate increases the no. of hours worked decreases, and amount paid increases.
Now since it has been given that relationship A has a greater rate than relationship B, so amount paid will also be greater for A than B.
so either option C or D is correct, as y =14.9x and y = 15.2x represent lesser or same amount paid as B.
The equation that relationship A represents is required.
The required relationship is B. [tex]y=15.2x[/tex]
Let [tex]x[/tex] be the hours worked and [tex]y[/tex] be the amount paid.
The ordered pairs are
[tex](2,30.4),(4,60.8),(5,76),(8,121.6)[/tex]
Let us find the slope between some of the ordered pairs
[tex]\dfrac{60.8-30.4}{4-2}=15.2[/tex]
[tex]\dfrac{76-60.8}{5-4}=15.2[/tex]
[tex]\dfrac{121.6-76}{8-5}=15.2[/tex]
The slopes are all equal.
So, the required relationship is B. [tex]y=15.2x[/tex]
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