Answer:
a) linear model is ![y= 800+(0.15)x](https://tex.z-dn.net/?f=y%3D%20800%2B%280.15%29x)
b) Amount earned by Samantha is $950.
Step-by-step explanation:
Given: Samantha base salary= $800
She get tips averaging 15% of the meals she serves.
Samantha serve meals worth a total of $1000.
Lets assume total worth of meal served by Samantha be "x".
And Total earning of samantha in a months be "y".
To calculate the total income of samantha, we need to add fixed income and variable income.
∴ ![y= fixed\ salary+ Tips\ on\ meals\ served](https://tex.z-dn.net/?f=y%3D%20fixed%5C%20salary%2B%20Tips%5C%20on%5C%20meals%5C%20served)
(∵ Tip is 15%)
∴ ![y= 800+(0.15)x](https://tex.z-dn.net/?f=y%3D%20800%2B%280.15%29x)
Hence, the linear model for the total earning of samantha is
.
Now, finding the total amount earned by samantha.
As given, Samantha serves meals worth a total of $1000.
Subtituting the value of meals worth in the equation.
![y= \$ 800+ (0.15)\times \$ 1000](https://tex.z-dn.net/?f=y%3D%20%5C%24%20800%2B%20%280.15%29%5Ctimes%20%5C%24%201000)
⇒![y= \$ 800+\$ 150](https://tex.z-dn.net/?f=y%3D%20%5C%24%20800%2B%5C%24%20150)
∴ y= $950
Hence, the total amount earned by Samantha is $950.