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? item cost price on the tag, x final cost $10 0.75(10) $20 0.75(20) $30 0.75(30) $40 0.75(40) 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. it is linear because the function is continuous. it is nonlinear because the final cost is determined by multiplying each price tag by 0.75. it is nonlinear because the price tag and final cost columns do not have the same common difference.
Answer
Explanation:
Step1: Recall linear - function definition
A linear function has a constant rate of change. If $y = mx + b$ (where $m$ is the slope and $b$ is the y - intercept), the rate of change $\frac{\Delta y}{\Delta x}=m$. In this case, let the price on the tag be $x$ and the final cost be $y$. The function is $y = 0.75x$, where $m = 0.75$ and $b = 0$.
Step2: Analyze the rate of change
When $x_1=10$, $y_1 = 0.75\times10 = 7.5$; when $x_2 = 20$, $y_2=0.75\times20 = 15$. The change in $x$ is $\Delta x=x_2 - x_1=20 - 10 = 10$, and the change in $y$ is $\Delta y=y_2 - y_1=15 - 7.5 = 7.5$. The ratio $\frac{\Delta y}{\Delta x}=\frac{7.5}{10}=0.75$. For any two - point change in $x$, the ratio of the change in $y$ to the change in $x$ is always $0.75$.
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.