Question

The ordered pairs (0,-3), (1,2), (2,7), (3,12) represent a function. What is a rule that represents this function. Could you also explain how to do it instead of just the answer.

Answer 1

Use any 2 sets of points...we are going to find the slope

slope = (y2 - y1) / (x2 - x1)
(1,2)....this is called set 1....so we will label it : x1 = 1 and y1 = 2
(2,7)...this is called set 2.....so we will label it : x2 = 2 and y2 = 7
now we sub into the formula
slope = (7 - 2) / (2 - 1) = 5/1 = 5

now we use y = mx + b
slope(m) = 5
use any set of ur points....(1,2)...x = 1 and y = 2
now we sub and find b, the y int
2 = 5(1) + b
2 = 5 + b
2 - 5 = b
-3 = b

so ur equation is : y = 5x - 3....or f(x) = 5x - 3 <== ur rule

and u will notice that if u sub in any of ur points into this equation, it will come out true