Question

example 4 write and solve a system of equations by graphing
cars suppose an electric car costs $29,000 to purchase and $0.036 per mile to drive, and a gasoline - powered car costs $19,000 to purchase and $0.08 per mile to drive. estimate after how many miles of driving the total cost of each car will be the same.
part a write equations for the total cost of owning each type of car.
let ( y = ) the total cost of owning the car and ( x = ) the number of miles driven.
so, the equation is ( y=x+ ) for the electric car and ( y=x+ ) for the gasoline car.
part b examine the graph to estimate the number of miles you would have to drive before the cost of owning each type of car would be same.
the graphs appear to intersect at approximately (, ).
this means that after driving about __ miles, the cost of owning each car will be the same.
think about it!
explain what the two equations represent in the context of the situation.

Explanation:

Step1: Ecuación para el coche eléctrico

La ecuación de costo total es \( y = mx + b \), donde \( m \) es el costo por milla y \( b \) es el costo inicial. Para el coche eléctrico, \( m = 0.036 \) y \( b = 29000 \), así que \( y = 0.036x + 29000 \).

Step2: Ecuación para el coche de gasolina

Para el coche de gasolina, \( m = 0.08 \) y \( b = 19000 \), entonces \( y = 0.08x + 19000 \).

Step3: Estimar la intersección

Observando el gráfico, la intersección parece ser en aproximadamente \( (225000, 37000) \). Esto significa que después de conducir aproximadamente \( 225000 \) millas, los costos son iguales.

Answer:

Para el coche eléctrico: \( y = 0.036x + 29000 \).
Para el coche de gasolina: \( y = 0.08x + 19000 \).
La intersección es aproximadamente \( (225000, 37000) \), y después de \( 225000 \) millas los costos son iguales.