Evan buys a new car that costs $23,740. Anna buys the same new car, only she buys the hybrid model. Anna’s hybrid car costs $31,140. Anna pre-pays for gasoline so that the cost for her gasoline will always be $2.40 per gallon forever. Using the graph, which represents a combined city and highway driving annual fuel usage, write an equation that represents the exact cost for any amount of miles she drives. Be sure to define the variables you are using for your equation.
On the y axis is "the gallons of fuel used". It goes up to 325. On the x axis is the "miles driven". It goes up to 13,000. There are two points, one at (6000,125) and the other at (12000,250)
To find the equation that represents the exact cost for any amount of miles Anna drives, we can use the given information and create a linear equation.
Let's first define the variables:
x = miles driven
y = gallons of fuel used
From the given graph, we have two points (6000, 125) and (12000, 250). These points represent the fuel usage for the corresponding miles driven.
Using these points, we can determine the slope (m) of the line:
m = (y2 - y1) / (x2 - x1)
m = (250 - 125) / (12000 - 6000)
m = 125 / 6000
m = 1/48
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the first point (6000, 125):
y - 125 = (1/48)(x - 6000)
Simplifying the equation:
y = (1/48)(x - 6000) + 125
y = (1/48)x - (1/48)(6000) + 125
y = (1/48)x - 125/48 + 6000/48
y = (1/48)x + 115/48
Therefore, the equation that represents the exact cost for any amount of miles Anna drives is:
Cost = (1/48)miles driven + 115/48
Note: This equation represents the fuel cost and not the total cost of driving.