Question

Is the relationship shown by the data linear? How can you tell if it is or is not? If so, model the data with an equation.

Answer 1

linear and y = 2x + 19

Explanation:

the x- values increment by 2 and the values of y increment by 4

This indicates a linear relationship exists in the form

y = mx + c ( m is the slope and c the y-intercept )

m =
`(rise)/(run)` =
`(4)/(2)` = 2

y = 2x + c ← is the partial equation

to find c use any ordered pair from the table

using (- 5, 9 ), then

9 = - 10 + c ⇒ c = 9 + 10 = 19

y = 2x + 19 ← linear equation

As a check

x = - 7 : y = - 14 + 19 = 5 ← correct value of y

x = - 5 : y = - 10 + 19 = 9 ← correct value of y

x = - 3 : y = - 6 + 19 = 13 ← correct value of y

x = - 1 : y = - 2 + 19 = 17 ← correct value of y