equations from patterns

[davidW]

Write an equation for the following function:

x 4 8 12 16 20
h(x) 1 2 3 4 5


I believe what I have here is a table of several ordered pairs. I know that I have to find the common differences of the domain and range. And then I have to write an equation using the ratio of the differences. And then I have to check my work. So would x be the domain and h(x) be the range?

domain: 8-4=4 and then I'm not sure whats next
range: 2-1=1


David

 

[skeeter]

change in x is 4

change in h(x) is 1

slope, m = [change in h(x)]/(change in x) = 1/4

h(x) = mx + b

h(x) = (1/4)x + b

pick any set of coordinates (x, h(x)), say (4, 1), and substitute into the above equation ...

1 = (1/4)(4) + b

solve for b ...

1 = 1 + b

b = 0

your equation is h(x) = (1/4)x