According to the table, the value of y increases by
= value of x increases by 1. It follows that the simplest equation relating y to x is linear and of the form
y=x+b for some constant b. Furthermore, the ordered pair
(1,) from the table must satisfy this equation. Substituting 1 for x and
for y in the equation
y=x+b gives
=(1)+b.solving for b gives
b=−.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,) is not a solution to the equation
y=x+2.Substituting 2 for x and
for y in this equation gives
=+2.which is false.