Question

What is the rule for the function shown in the table?

Answer 1

Answer:

y = - 3x - 2

Step-by-step explanation:

The function is linear and can be expressed in slope- intercept form

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

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (- 1, 1) ← 2 ordered pairs from the table

m = $\frac{1-4}{-1-(-2)}$ = $\frac{-3}{-1+2}$ = $\frac{-3}{1}$ = - 3 , then

y = - 3x + c

To find c substitute any ordered pair into the equation

using (0, - 2 ) , then

- 2 = - 3(0) + c = 0 + c ⇒ c = - 2

y = - 3x - 2 ← function rule