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) |\nit is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.\nit is linear because the function is continuous.\nit is nonlinear because the final cost is determined by multiplying each price tag by 0.75.\nit is nonlinear because the price tag and final cost columns do not have the same common difference.
Answer
Explanation:
Step1: Definir la función
Sea $x$ el precio en la etiqueta. La función que representa el costo final $y$ es $y = 0.75x$.
Step2: Analizar la forma de la función
Una función lineal tiene la forma $y=mx + b$, donde $m$ es la pendiente y $b$ es la intersección con el eje - y. En la función $y = 0.75x$, $m = 0.75$ y $b = 0$.
Step3: Comprobar la razón de cambio
La razón de cambio (pendiente) entre cualquier par de puntos $(x_1,y_1)$ y $(x_2,y_2)$ en la función $y = 0.75x$ es $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0.75x_2-0.75x_1}{x_2 - x_1}=0.75$, que es constante.
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.