Question

Input 1 2 3 4 output -8 -11 -14 -17 what is the rule

Answer 1

The function rule is:
`y = -3x-5`

Explanation:

Using the given input/output values, we can take two pairs of input-output values for finding the rule.

The function is a linear function as the input and output are changing linearly.

Required pairs are:

(1,-8) and (2, -11)

The general rule for linear function is:

`y = mx+b`

m is the slope of the function calculated using the formula

`m = (y_2-y_1)/(x_2-x_1)`

Putting the values

`m = (-11+8)/(2-1)\\m = (-3)/(1)\\m = -3`

Putting in equation

`y = -3x+b`

To find the value of b, putting (1,-8) in the equation

`-8 = -3(1) +b\\-8 = -3+b\\-8+3 = b\\b = -5`

Putting the values

`y = -3x-5`

Hence,

The function rule is:
`y = -3x-5`