SAT Math · Two-variable data: models and scatterplots · easy
The equation C = 3.5g + 40 models the total cost C, in dollars, of a rental car after driving g gallons' worth of fuel, including a fixed…
The equation models the total cost , in dollars, of a rental car after driving gallons' worth of fuel, including a fixed rental fee. What does the value 3.5 represent in this model?
Answer and explanation
Answer: C: The cost, in dollars, increases by $3.50 for each additional gallon of fuel used.
In , the cost depends linearly on , the gallons of fuel. The coefficient of is the slope, which is the rate of change: each additional gallon adds $3.50 to the total cost. That is choice C. The constant 40 is the starting cost when , the fixed fee. Choice A claims 3.5 is the total cost, but total cost changes with . Choice B mentions days, but the variable is gallons. Choice D says 3.5 is the initial fee, but the initial fee is 40, the intercept. Slope means rate; intercept means starting amount.
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