Question

The ordered pairs (0,-3), (1,2), (2,7), (3,12) represent a function. What is a rule that represents this function?

Answer 1

Note that y increases 5 when x increases 1. So, the rule will look like

y = 5x

But, when x=0, 5x=0 and we want y = -3.

So,

y = 5x-3

Answer 2

You have to look for some pattern
Did you notice that for every 1 unit increase in the x's there is a 5 unit increase in the y's

so you know it starts with
y = 5x + b, we still don't know the b
plug in one of the points , how about (1,2)
2 = 5(1) + b
b = -3

function:
y = 5x - 3 or
f(x) = 5x - 3