Question

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

Input x -2, -1, 0, 1, 2
Output y 4, 1, -2, -5, -8
y = -2 x
y = x – 6
y = -3 x - 2
y = -2 x – 2

Answer 1

y = - 3x - 2

Explanation:

Answer 2

y = - 3x - 2

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 =
`(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 =
`(1-4)/(-1-(-2))` =
`(-3)/(-1+2)` =
`(-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