a printer will produce 80 wedding invitations for $210. the price to produce 120 invitations is $290. the…

a printer will produce 80 wedding invitations for $210. the price to produce 120 invitations is $290. the printer uses a linear function to determine the price for producing different amounts of invitations. how much will the printer charge to produce 60 invitations?\n$120.00\n$145.00\n$157.50\n$170.00

a printer will produce 80 wedding invitations for $210. the price to produce 120 invitations is $290. the printer uses a linear function to determine the price for producing different amounts of invitations. how much will the printer charge to produce 60 invitations?\n$120.00\n$145.00\n$157.50\n$170.00

Answer

Explanation:

Step1: Encontrar la pendiente de la función lineal

Sean $(x_1,y_1)=(80,210)$ y $(x_2,y_2)=(120,290)$. La fórmula de la pendiente $m$ es $m=\frac{y_2 - y_1}{x_2 - x_1}$. Entonces $m=\frac{290 - 210}{120 - 80}=\frac{80}{40}=2$.

Step2: Encontrar la ecuación de la recta en la forma $y=mx + b$

Usamos el punto - pendiente $y - y_1=m(x - x_1)$ con $(x_1,y_1)=(80,210)$ y $m = 2$. $y-210=2(x - 80)$ $y-210=2x-160$ $y=2x + 50$.

Step3: Calcular el costo para 60 invitaciones

Sustituimos $x = 60$ en la ecuación $y=2x + 50$. $y=2\times60+50=120 + 50=170$.

Answer:

$170.00$