Question

In2002, the price of a gallon of gas, y, is estimated to be $1.50 based on the equation y = 1.40x. What does x represent in this context?

a) The year
b) The price of gas in 2001
c) The price of gas in 2002
d) The average price of gas in 2001

Answer 1

Main Answer:

The variable
`\(x\) in \(y = 1.40x\)` corresponds to the year, pinpointing 2002. It signifies the independent variable in the equation representing the estimated gas price
`(\(y\)).` c) The price of gas in 2002.

Therefore, the correct answer is c) The price of gas in 2002.

Explanation:

In the given equation
`\(y = 1.40x\), \(x\)` represents the independent variable, which is the year. Therefore, the correct answer is (c) "The price of gas in 2002." This interpretation aligns with the standard form of a linear equation, where
`\(y\)` is the dependent variable and
`\(x\)` is the independent variable. In this context, the equation suggests that the price of gas
`(\(y\))`is estimated to be $1.50 in the year represented by
`\(x\`), which is 2002.

The coefficient of
`\(x\)`, which is 1.40, indicates the rate of change in the price of gas with respect to the year. In this case, it implies that for each unit increase in the year
`(\(x\)),` the price of gas
`(\(y\))` will increase by $1.40. Therefore,
`\(x\)` is a representation of time or the specific year, leading us to conclude that it corresponds to the year 2002.

In summary, the value of
`\(x\)` in the equation
`\(y = 1.40x\`) refers to the specific year, and in this context, it represents the year 2002.

Therefore, the correct answer is c) The price of gas in 2002.

Answer 2

Main Answer:

In the context of the given equation, x represents the year, specifically the year 2001.The option D is correct.

Explanation:

The equation provided, y = 1.40x, is a linear equation that shows the relationship between the price of gas (y) and the year (x). In 2001, the price of gas was not explicitly stated in the equation, but it can be calculated using the value of x when it is set to 2001.

When x is equal to 2001, the price of gas (y) is estimated to be $1.40x, which in this case would be $1.40(2001), or $2,800. Since this is an estimate and not an exact value, the price of gas in 2001 is likely to have been slightly different than this calculation suggests.

However, this equation provides a general idea of how the price of gas changed over time during this period.The option D is correct.