Question

IN (3)

2
10
6
7
-3
-10 1000
15
OUT (9)
9 25 17
a. Explain in words what is done to the input value (20) to produce the output value (y).
b. Write the rule you described in part (a) with algebraic symbols.

Answer 1

(a) Rule: Multiply the input (x) by 2 and add 5 to the result of the product

(b)
`y =2x +5`

Explanation:

Given

The attached table

Solving (a): The rule of the table in words

First, we calculate the slope (m)

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

Using:

`(x_1,y_1) = (2,9)`

`(x_1,y_1) = (10,25)`

So, we have:

`m = (25 - 9)/(10 - 2)`

`m = (16)/(8)`

`m=2`

The equation is calculated using:

`y - y_1 =m(x - x_1)`

Using:

`(x_1,y_1) = (6,17)`

We have:

`y - 17 =2(x - 6)`

`y - 17 =2x - 12`

Make y the subject

`y =2x - 12+17`

`y =2x +5`

Hence, the rule is:

Multiply the input (x) by 2 and add 5 to the result of the product

(b): The rule, in algebra

As solved in (a), the rule is:

`y =2x +5`