a) To write a linear function that relates the number of gallons G left in the tank after a journey of x miles, we need to determine the rate at which the car burns gasoline.
Since the car burns 5 gallons for every 100 miles, we can calculate the rate of gasoline consumption as 5 gallons/100 miles. This means that for every 100 miles driven, the car consumes 5 gallons of gasoline.
Now, let's set up the linear function. Since the amount of gasoline in the tank decreases linearly, we can use the slope-intercept form of a linear equation: y = mx + b, where y represents the number of gallons G left in the tank and x represents the number of miles driven.
The slope (m) of the linear function represents the rate at which the gasoline is being consumed. In this case, the slope is -5 gallons/100 miles because the amount of gasoline decreases as the number of miles driven increases.
The y-intercept (b) represents the initial amount of gasoline in the tank. In this case, the initial amount is 30 gallons.
Therefore, the linear function that relates the number of gallons G left in the tank after a journey of x miles is:
G(x) = -5x + 30
b) The slope of the graph of G represents the rate at which the gasoline is being consumed. In this case, the slope is -5 gallons/100 miles.
The negative sign indicates that the amount of gasoline in the tank decreases as the number of miles driven increases.
So, the slope of the graph of G tells us that for tells us that for every 100 miles driven, the car consumes 5 gallons of gasoline.
Answers & Comments
Answer:
a) To write a linear function that relates the number of gallons G left in the tank after a journey of x miles, we need to determine the rate at which the car burns gasoline.
Since the car burns 5 gallons for every 100 miles, we can calculate the rate of gasoline consumption as 5 gallons/100 miles. This means that for every 100 miles driven, the car consumes 5 gallons of gasoline.
Now, let's set up the linear function. Since the amount of gasoline in the tank decreases linearly, we can use the slope-intercept form of a linear equation: y = mx + b, where y represents the number of gallons G left in the tank and x represents the number of miles driven.
The slope (m) of the linear function represents the rate at which the gasoline is being consumed. In this case, the slope is -5 gallons/100 miles because the amount of gasoline decreases as the number of miles driven increases.
The y-intercept (b) represents the initial amount of gasoline in the tank. In this case, the initial amount is 30 gallons.
Therefore, the linear function that relates the number of gallons G left in the tank after a journey of x miles is:
G(x) = -5x + 30
b) The slope of the graph of G represents the rate at which the gasoline is being consumed. In this case, the slope is -5 gallons/100 miles.
The negative sign indicates that the amount of gasoline in the tank decreases as the number of miles driven increases.
So, the slope of the graph of G tells us that for tells us that for every 100 miles driven, the car consumes 5 gallons of gasoline.
Step-by-step explanation:
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