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Algebra Linear Function Example 1

Question:

A car fills up at a gas station near the highway and drive at a constant speed. The following chart is the relationship between driving time and remaining oil in the fuel tank. When the car drives 3.3 hours, how many gallons of gasoline is left in the fuel tank?

Driving time x (hour) 0 1 1.5 2.5
Remaining oil y (gallon) 40 30 25 15

Solution>

The chart is the relationship between Driving time and Remaining oil. Now we draw the four points. The first point, x = 0, y = 40. The second point, x = 1, y = 30. The third point, x = 1.5, y = 25. The fourth point, x = 2.5, y = 15. Connect these four points, we found that the relationship between x and y is linear relation, so, we can use a linear function to express the remaining oil and the driving time. The linear function is y = k + b, in which, k is the slope of the line and b is the y-intercept of the line. To determine the values of k and b, we use these two points (0, 40) and (1, 30).

substitute (0. 40) into the equation y = k x + b
40 = k × 0 + b
b = 40
substitute (1, 30) into the equation y = k x + 40
30 = k × 1 + 40
k = 30 - 40 = -10
so, the linear equation is: y = -10 k + 40
when x = 3.3, y = -10 × 3.3 + 40 = 7

Therefore, when the car drives 3.3 hours, the remaining oil in the fuel tank is 7 gallons. Please see video for more detail answer.