Answer:
The function rule is: [tex]y = -3x-5[/tex]
Step-by-step 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:
[tex]y = mx+b[/tex]
m is the slope of the function calculated using the formula
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Putting the values
[tex]m = \frac{-11+8}{2-1}\\m = \frac{-3}{1}\\m = -3[/tex]
Putting in equation
[tex]y = -3x+b[/tex]
To find the value of b, putting (1,-8) in the equation
[tex]-8 = -3(1) +b\\-8 = -3+b\\-8+3 = b\\b = -5[/tex]
Putting the values
[tex]y = -3x-5[/tex]
Hence,
The function rule is: [tex]y = -3x-5[/tex]
