Any answers for 3-6 ? and how to find a rule ? and what is a rule ? ( be specific )

To find a function (rule) for data you first seek to find its rate of change...

dy/dx=(11-5)/(14-8), (5-0)/(8-3)

dy/dx=1, 1  so this is a constant rate of change for the first derivative which means that it is just a line of the form:

y=mx+b  and we found above that m, dy/dx, the slope was just one so:

y=x+b, and using any point we can solve for b, the y-intercept, use (3,0)

0=3+b, so b=-3 and the "rule" is:

y=x-3  (the missing point was (7,4))

...

This next one you can just look at and see that it increases by one every time x increases by one so again you have a line of the form

y=x+b, using point (3,7) we solve for the y-intercept...

7=3+b, so b=4 and the rule is:

y=x+4  and the missing term was (12,16)

...

Uh, actually all of these tables have lines with a slope one... :P  so you really only need to find the y-intercepts and find the missing points...

...

y=x+b and using point (5,9)

9=5+b, b=4 and the line is

y=x+4, so the missing point is (14,18)



y=x+b and using point (14,16)

16=14+b, so b=2 so the line is:

y=x+2, and the missing term is (6,8)