Producción de vehículos. En en el año 2000 FIAT produjo 1,135 autos y en el año 2010, produjo 1,825 autos. Teniendo un crecimiento lineal cada año. Determina un modelo lineal (Ecuación General) de dicho comportamiento de producción de autos con los datos que se proporcionan.

Answer:

El modelo lineal del comportamiento de producción de autos es y=69*x -136865

Step-by-step explanation:

Una función real de variable real es una función lineal si es de la forma f(x)=mx+n o y=mx+n. Es decir, la ecuación de la función se corresponde con un polinomio de primer grado. La representación gráfica de una función lineal es siempre una recta. El coeficiente m recibe el nombre de pendiente de la recta y será el responsable de lo inclinada o “pendiente” que se encuentre la recta respecto del eje X mientras que b es el intercepto con el eje Y.

Teniendo dos puntos (x1,y1) y (x2,y2) se puede calcular la pendiente mediante la expresión:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Para encontrar el valor de b, una vez reemplazado el valor de m en la ecuación se sustituye los valores de x y de y por los valores de las coordenadas de uno de los puntos, sea el uno o el dos y se despeja b para así obtener su valor.

En este caso y representará la producción de autos mientras que x cada año de producción. Entonces se tiene los siguientes puntos: (2000; 1135) y (2010; 1825)

Por consiguiente, el valor de m será:

[tex]m=\frac{1825-1135}{2010-2000}[/tex]

m=69

Entonces: y=69*x + b. Eligiendo el punto (2000; 1135) y reemplazando:

1135= 69*2000 + b

Se obtiene que el valor de b es:

1135= 138000 + b

-136865= b

Entonces el modelo lineal del comportamiento de producción de autos es y=69*x -136865

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