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An electric bicycle manufacturer produces 6,000 units when the market price is US$2,350, while if the market price is US$1,750 it produces 4,200 units. The linear function that represents this situation is

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Answer to a math question An electric bicycle manufacturer produces 6,000 units when the market price is US$2,350, while if the market price is US$1,750 it produces 4,200 units. The linear function that represents this situation is

Expert avatar
Timmothy
4.8
99 Answers
To find the linear function that represents this situation, we need to determine the slope of the line using the two given data points.

Let:
- x_1 = 2350 (market price of US$2,350)
- y_1 = 6000 (number of units produced when market price is US$2,350)
- x_2 = 1750 (market price of US$1,750)
- y_2 = 4200 (number of units produced when market price is US$1,750)

The slope of the line can be calculated as:
m = \dfrac{y_2 - y_1}{x_2 - x_1}

Substitute the given values into the formula:
m = \dfrac{4200 - 6000}{1750 - 2350} = \dfrac{-1800}{-600} = 3

Now that we have the slope, we can use the point-slope form of a linear equation to write the equation of the line:
y - y_1 = m(x - x_1)

Substitute one of the points and the slope into the equation:
y - 6000 = 3(x - 2350)
y - 6000 = 3x - 7050
y = 3x - 1050

Therefore, the linear function that represents this situation is y =3x-1050

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