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Which of the following equations relates...


Which of the following equations relates y to x for the values in the table above?

A

`y=1/2.(5/2)^x`

B

`y=2.(3/4)^x`

C

`y=3/4x+2`

D

`y=7/2x-3/4`

Text Solution

Verified by Experts

The correct Answer is:
D
According to the table, the value of y increases by `14/4=7/2` every time the value of x increases by 1. It follows that the simplest equation relating y to x is linear and of the form `y=7/2x+b` for some constant b. Furthermore, the ordered pair `(1,11/4)` from the table must satisfy this equation. Substituting 1 for x and `11/4` for y in the equation `y=7/2x+b` gives `11/4=7/2(1)+b`. Solving this equation for b gives `b=-3/4`. Therefore the equation in choice D correctly relates y to x.
Choices A and B are incorrect. The relationship between x and y cannot be exponential because the differences, not the ratios, of y-values are the same every time the x-values change by the same amount. Choice C is incorrect because the ordered pair `(2,25/4)` is not a solution to the equation `y=3/4x+2`. Substituting 2 for x and `25/4` for y in this equation gives `25/4=3/2+2`, which is false.
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