Answer:
(a) Rule: Multiply the input (x) by 2 and add 5 to the result of the product
(b) [tex]y =2x +5[/tex]
Step-by-step explanation:
Given
The attached table
Solving (a): The rule of the table in words
First, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Using:
[tex](x_1,y_1) = (2,9)[/tex]
[tex](x_1,y_1) = (10,25)[/tex]
So, we have:
[tex]m = \frac{25 - 9}{10 - 2}[/tex]
[tex]m = \frac{16}{8}[/tex]
[tex]m=2[/tex]
The equation is calculated using:
[tex]y - y_1 =m(x - x_1)[/tex]
Using:
[tex](x_1,y_1) = (6,17)[/tex]
We have:
[tex]y - 17 =2(x - 6)[/tex]
[tex]y - 17 =2x - 12[/tex]
Make y the subject
[tex]y =2x - 12+17[/tex]
[tex]y =2x +5[/tex]
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:
[tex]y =2x +5[/tex]
