In the linear function h , h ( 0 ) = 41 and h ( 1 ) = 40 .

Question

In the linear function h , h ( 0 ) = 41 and h ( 1 ) = 40 . Which equation defines h ?

Accepted Answer

Choice A is correct. An equation defining a linear function can be written in the form h x = a x + b , where a and b are constants. It&rsquo;s given that h 0 = 41 . Substituting 0 for x and 41 for h x in the equation h x = a x + b yields 41 = a 0 + b , or b = 41 . Substituting 41 for b in the equation h x = a x + b yields h x = a x + 41 . It&rsquo;s also given that h 1 = 40 . Substituting 1 for x and 40 for h x in the equation h x = a x + 41 yields 40 = a 1 + 41 , or 40 = a + 41 . Subtracting 41 from the left- and right-hand sides of this equation yields - 1 = a . Substituting - 1 for a in the equation h x = a x + 41 yields h x = - 1 x + 41 , or h x = - x + 41 . Choice B is incorrect. Substituting 0 for x and 41 for h x in this equation yields 41 = - 0 , which isn't a true statement. Choice C is incorrect. Substituting 0 for x and 41 for h x in this equation yields 41 = - 41 0 , or 41 = 0 , which isn't a true statement. Choice D is incorrect. Substituting 41 for h x in this equation yields 41 = - 41 , which isn't a true statement.

Question 61063a