Question

Type an equation for the following pattern....

x...1, 2, 3, 4, 5
y...21/2, 9, 15/2, 6, 9/2

y=-3/2x + ?

Answer 1

y=-3/2 + ?

21/2=-3/2 + ?
-?= -3/2-21/2
-?= -24/2
-?=-12
?=12


The equation is y=-3/2x + 12

Answer 2

see explanation

Explanation:

This is a linear pattern with the equation in the form

y = mx + c

To find m use the points (2, 9) and (4, 6) and the formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

m =
`(6-9)/(4-2)` =
`(-3)/(2)` = -
`(3)/(2)`, thus

y = -
`(3)/(2)` x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation.

Using (2, 9), then

9 = - 3 + c ⇒ c = 9 + 3 = 12

y = -
`(3)/(2)` x + 12 ← equation for pattern