Question

which equation gives the relationship between x and y in the table below?

x	y
-2	-8
-1	-4
0	0
1	4
2	8

• $x = y + 4$
• $y = x + 4$
• $x = 4y$
• $y = 4x$

Explanation:

Step1: Test first pair (-2,-8)

Substitute $x=-2$ into each option:

• $x=y+4$: $-2=-8+4 \implies -2=-4$ (False)
• $y=x+4$: $-8=-2+4 \implies -8=2$ (False)
• $x=4y$: $-2=4(-8) \implies -2=-32$ (False)
• $y=4x$: $-8=4(-2) \implies -8=-8$ (True)

Step2: Verify second pair (-1,-4)

Substitute $x=-1$ into $y=4x$:
$y=4(-1) = -4$ (Matches the table)

Step3: Verify third pair (0,0)

Substitute $x=0$ into $y=4x$:
$y=4(0) = 0$ (Matches the table)

Step4: Verify fourth pair (1,4)

Substitute $x=1$ into $y=4x$:
$y=4(1) = 4$ (Matches the table)

Step5: Verify fifth pair (2,8)

Substitute $x=2$ into $y=4x$:
$y=4(2) = 8$ (Matches the table)

Answer:

D. $y = 4x$