Question

Which function rule represents the data in the table? X -3, -2, -1, 0, 1. Y -1, 2, 5, 8, 11. How do I find the answer?

Answer 1

( - 3, - 1 ) , ( - 2 , 2 ) , ( - 1 , 5 ) , ( 0 , 8 ) , ( 1, 11 )

Change of x:

- 2 - ( - 3 ) = - 2 + 3 = 1

- 1 - ( - 2 ) = - 1 + 2 = 1

0 - ( - 1 ) = 0 + 1 = 1

1 - 0 = 0


Change of y:

2 - ( - 1 ) = 2 + 1 = 3

5 - 2 = 3

8 - 5 = 3

11 - 8 = 3

When x change 1 y change 3

Slope m = y / x = 3 / 1 = 3

Now straight line equation slope-intercept form:

y = m x + b

where b is y coordinate for x = 0 ( y- intercept)

for x = 0 y = 8

so

y = 3 ∙ 0 + b = 0 + 8 = 8

b = 8

y = m x + b

y = 3 x + 8

Answer 2

Indeed when x change for ∆x = 1 y is change for ∆y = 3

m = ∆y / ∆x = 3 / 1 = 3