the final cost of a sale item is determined by multiplying the price on the tag by 75%. which best describes…
the final cost of a sale item is determined by multiplying the price on the tag by 75%. which best describes the function that represents the situation?\nitem cost\n| price on the tag, x | final cost |\n| ---- | ---- |\n| $10 | 0.75(10) |\n| $20 | 0.75(20) |\n| $30 | 0.75(30) |\n| $40 | 0.75(40) |\no it is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.\no it is linear because the function is continuous.\no it is nonlinear because the final cost is determined by multiplying each price tag by 0.75.\no it is nonlinear because the price tag and final cost columns do not have the same common difference.
Answer
Explanation:
Step1: Define variables
Let $x$ be the price on the tag and $y$ be the final cost. Then $y = 0.75x$.
Step2: Recall linear - function properties
A linear function has the form $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. In $y = 0.75x$, $m = 0.75$ and $b = 0$.
Step3: Check the rate of change
The rate of change (slope) between any two points $(x_1,y_1)$ and $(x_2,y_2)$ for the function $y = 0.75x$ is $\frac{y_2 - y_1}{x_2 - x_1}=\frac{0.75x_2-0.75x_1}{x_2 - x_1}=0.75$, which is constant.
Answer:
It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.