Question

Suppose that you get your car’s gas tank filled up, then drive off down the highway. As you drive, the number of minutes, t, since you had the tank filled, and the number of liters, g, remaining in the tank are related by a linear function. After 40 minutes you have 52 liters left.

a. An hour after the fill-up you have 40 liters left. Write the equation for this function.
b. What is the g-intercept?

Answer 1

The equation of the linear function between time (t) and remaining gas (g) is g = -0.6t + 76. The g-intercept of this function is 76 liters, meaning the tank was originally filled with 76 liters of gasoline.

Step-by-step explanation:

The student is asking about a linear function that represents the relationship between the time since the gas tank was filled (t) and the remaining gas in the tank (g). We are given two points: (40, 52) and (60, 40). We can use these to find the slope (m) of the line using the formula m = (g2 - g1) / (t2 - t1). So m = (40 - 52) / (60 - 40) which simplifies to m = -12 / 20 = -0.6.

With the slope and one point, we can use the point-slope form to establish the equation: g - g1 = m(t - t1). Substituting gives g - 52 = -0.6(t - 40). This simplifies to g = -0.6t + 76, which is the equation of the linear function.

To find the g-intercept, set t to 0 in the equation g = -0.6t + 76, which yields g = 76. Therefore, the g-intercept is 76 liters, indicating that the car's tank was filled with 76 liters of gasoline initially.