Question

look at the table below:

x	y
2	8
4	4
8	2

which equation matches this table?

• $y = \frac{16}{x}$
• $y = 4x$
• $y = 2x^2$
• $y = x + 6$

Explanation:

Step1: Test \( y = \frac{16}{x} \)

Substitute \( x = 2 \): \( y=\frac{16}{2}=8 \) (matches table).
Substitute \( x = 4 \): \( y=\frac{16}{4}=4 \) (matches table).
Substitute \( x = 8 \): \( y=\frac{16}{8}=2 \) (matches table).

Step2: Test \( y = 4x \)

Substitute \( x = 2 \): \( y = 4\times2 = 8 \) (matches).
Substitute \( x = 4 \): \( y = 4\times4 = 16
eq 4 \) (does not match).

Step3: Test \( y = 2x^2 \)

Substitute \( x = 2 \): \( y = 2\times2^2 = 8 \) (matches).
Substitute \( x = 4 \): \( y = 2\times4^2 = 32
eq 4 \) (does not match).

Step4: Test \( y = x + 6 \)

Substitute \( x = 2 \): \( y = 2 + 6 = 8 \) (matches).
Substitute \( x = 4 \): \( y = 4 + 6 = 10
eq 4 \) (does not match).

Answer:

\( y = \frac{16}{x} \) (the first option)