Question

complete the missing entries in the table below. then write the rule.

in (x)	out (y)
2	4
10	28
6	16
7
-3
	10
-10
100
z

Explanation:

Step1: Find the relationship rule

Test with given pairs:
For $x=2, y=4$: $3(2)-2=4$
For $x=10, y=28$: $3(10)-2=28$
For $x=6, y=16$: $3(6)-2=16$
Rule: $y=3x-2$

Step2: Calculate $y$ for $x=7$

$y=3(7)-2=21-2=19$

Step3: Calculate $y$ for $x=-3$

$y=3(-3)-2=-9-2=-11$

Step4: Calculate $x$ for $y=10$

$10=3x-2 \implies 3x=12 \implies x=4$

Step5: Calculate $y$ for $x=-10$

$y=3(-10)-2=-30-2=-32$

Step6: Calculate $y$ for $x=100$

$y=3(100)-2=300-2=298$

Step7: Express $y$ for $x=x$

$y=3x-2$

Answer:

IN ($x$)	OUT ($y$)
10	28
6	16
7	19
-3	-11
4	10
-10	-32
100	298
$x$	$3x-2$

Rule: $y=3x-2$