Question

In January 2007, there were 71,000 registered gasoline- electric hybrid cars in the United States. In 2004, there were only 29,000 registered gasoline-electric hybrids. (Source: U.S. Energy Information Administration)

Write an equation describing the relationship between time and number of registered gasoline-hybrid cars. Use ordered pairs of the form (years past 2004, number of cars).

Answer 1

The equation describing the relationship between time since 2004 and the number of registered gasoline-hybrid cars is y = 14000x + 29000, where x represents the years since 2004 and y is the number of cars.

Step-by-step explanation:

The relationship between time and the number of registered gasoline-hybrid cars can be represented by a linear equation, derived from two given points. These points represent the number of cars in given years: (0, 29000) for the year 2004 and (3, 71000) for the year 2007, where the first value in each ordered pair is the number of years past 2004, and the second value represents the number of gasoline-hybrid cars.

To find the linear equation, we calculate the slope (m) of the line:

m = (71000 - 29000) / (3 - 0) = 42000 / 3 = 14000

Now, we use the point-slope form to write the equation of the line:
y - y1 = m(x - x1)

Replacing y1 with 29000 and x1 with 0, and using the calculated slope:

y - 29000 = 14000(x - 0)
y = 14000x + 29000

This equation describes the relationship between the time since 2004 and the number of registered gasoline-hybrid cars.

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