Question

1. which equation corresponds to the value pairs in the table below?

x	y
1	4
5	28
7	52
9	84
10	103
100	10,003

○ y = x²
○ y = x + 3
○ y = 10x + 3
○ y = x²+ 3

Explanation:

Step1: Test first pair (x = 0.5, y = 3.25)

For $y=x^{2}$, $y=(0.5)^{2}=0.25
eq3.25$. For $y = x + 3$, $y=0.5 + 3=3.5
eq3.25$. For $y=10x + 3$, $y=10\times0.5+3=8
eq3.25$. For $y=x^{2}+3$, $y=(0.5)^{2}+3=0.25 + 3=3.25$.

Step2: Test second pair (x = 1, y = 4)

For $y=x^{2}+3$, when $x = 1$, $y=1^{2}+3=1 + 3=4$.

Step3: Test third pair (x = 5, y = 28)

For $y=x^{2}+3$, when $x = 5$, $y=5^{2}+3=25 + 3=28$.

Step4: Test fourth pair (x = 7, y = 52)

For $y=x^{2}+3$, when $x = 7$, $y=7^{2}+3=49+3=52$.

Step5: Test fifth pair (x = 9, y = 84)

For $y=x^{2}+3$, when $x = 9$, $y=9^{2}+3=81 + 3=84$.

Step6: Test sixth pair (x = 10, y = 103)

For $y=x^{2}+3$, when $x = 10$, $y=10^{2}+3=100 + 3=103$.

Step7: Test seventh pair (x = 100, y = 10003)

For $y=x^{2}+3$, when $x = 100$, $y=100^{2}+3=10000+3=10003$.

Answer:

$y=x^{2}+3$