Question

Which function represents the relationship shown in the table?
|x| 1 | 2 | 3 | 4 |
|y| 3 | 1 |-1 |-3 |

The answer is a equation

Answer 1

x1 = 1 , y1 = 3

x2 = 2 , y2 = 1

x3 = 3 , y3 = - 1

x4 = 4 , y4 = - 3


m = rate  of  change = change  y / change   x


m = ( y2 - y1 ) / (  x2 - x1 ) = ( 1 - 3 ) / ( 2 - 1 ) = - 2 / 1 = - 2

m = ( y3 - y2 ) / (  x3 - x2 ) = ( - 1 - 1 ) / ( 3 - 2 ) = - 2 / 1 = - 2

m = ( y4 - y3 ) / ( x4 - x3 ) = [ - 3 - ( - 1 ) ] / ( 4 - 3 ) = ( - 3 + 1 ) / 1 = - 2 / 1 = - 2


A linear function y = m x + b has a constant rate of change.

In this case:

x1 = 1 , y1 = 3

y = m x + b

3 = ( - 2 ) ∙ 1 + b

3 = - 2 + b

Add 2 to both sides

5 = b

b = 5

Your linear function y = m x + b is:

y = - 2 x + 5

You can check that:

x1 = 1 , y = - 2 ∙ 1 + 5 = - 2 + 5 = 3 , y1 = 3

x2 = 2 , y = - 2 ∙ 2 + 5 = - 4 + 5 = 1 , y2 = 1

x3 = 3 , y = - 2 ∙ 3 + 5 = - 6 + 5 = - 1 , y3 = - 1

x4 = 4 , y = - 2 ∙ 4 + 5 = - 8 + 5 = - 3 , y4 = - 3


So the answer is:

y = - 2 x + 5