Question

select the correct answer. which equation best models the set of data in this table?

x	0	1	2	3	4	5	6	7	8	9
y	32	67	79	91	98	106	114	120	126	132

a. $y = 33sqrt{x}-32.7$
b. $y = 33x + 32.7$
c. $y = 33x - 32.7$
d. $y = 33sqrt{x}+32.7$

Explanation:

Step1: Substitute x = 0

When \(x = 0\), for option A: \(y=33\sqrt{0}-32.7=- 32.7\); for option B: \(y = 33\times0+32.7 = 32.7\); for option C: \(y=33\times0 - 32.7=-32.7\); for option D: \(y = 33\sqrt{0}+32.7=32.7\). In the table, when \(x = 0\), \(y = 32\), so options A and C can be eliminated since they give non - matching values when \(x = 0\).

Step2: Substitute x = 1

For option B: \(y=33\times1 + 32.7=65.7\). For option D: \(y=33\sqrt{1}+32.7=33 + 32.7=65.7\).

Step3: Substitute x = 9

For option B: \(y=33\times9+32.7=297+32.7 = 329.7\). For option D: \(y=33\sqrt{9}+32.7=33\times3+32.7=99 + 32.7=131.7\approx132\) (close to the value in the table when \(x = 9\)).

Answer:

D. \(y = 33\sqrt{x}+32.7\)