Jenny is driving on the highway. She begins the trip with 18 gallons of gas in her car. The car uses up one gallon of gas every 35 miles.Let G represent the number of gallons of gas she has left in her tank, and let D represent the total distance (in miles) she has traveled. Write an equation relating G to D, and then graph your equation using the axes below.Equation:
Question
Jenny is driving on the highway. She begins the trip with 18 gallons of gas in her car. The car uses up one gallon of gas every 35 miles.Let G represent the number of gallons of gas she has left in her tank, and let D represent the total distance (in miles) she has traveled. Write an equation relating G to D, and then graph your equation using the axes below.Equation:
Solution
The equation that relates G (gallons of gas left) to D (distance traveled) can be derived from the information given in the problem.
We know that Jenny starts with 18 gallons of gas and that she uses 1 gallon of gas every 35 miles. This means that for every mile she drives, she uses 1/35 of a gallon of gas.
So, the amount of gas used, in gallons, is D/35.
Since she starts with 18 gallons, the amount of gas left, G, after driving D miles is the initial amount of gas minus the amount of gas used.
So, the equation relating G to D is:
G = 18 - D/35
To graph this equation, you would plot G on the y-axis and D on the x-axis. The graph would start at the point (0,18) (since she starts with 18 gallons of gas and has traveled 0 miles) and would slope downwards, indicating that the amount of gas is decreasing as the distance traveled increases. The slope of the line would be -1/35, reflecting the rate at which gas is used up.
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