Let's analyze the given linear equation:
\[ y = 0.2x + 15 \]
Here, \( y \) represents the average temperature (in Celsius), and \( x \) represents the number of years since 2000.
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Identify the slope: The coefficient of \( x \) (which is 0.2) indicates the average increase in temperature per year. Thus, the average increase in temperature each year is 0.2°C, not 1°C.
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Finding temperature in 2010:
- For 2010, \( x = 2010 - 2000 = 10 \)
- Plugging it into the equation: \[ y = 0.2(10) + 15 = 2 + 15 = 17°C \] Thus, the statement about the temperature in 2010 is true.
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Temperature increase from 2029 to 2030:
- The equation indicates a consistent increase of 0.2°C per year. Therefore, in 2030, the temperature will be 0.2°C higher than in 2029, not 1°C. So, this statement is false.
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Average increase every 5 years:
- Over 5 years, the temperature will increase by \( 5 \times 0.2 = 1°C \). Thus, the average increase in temperature every 5 years is true.
Summary of True Statements:
- \( y = 0.2x + 15 \) represents the linear equation. (True)
- In the year 2010, the temperature was 17 °C. (True)
- If the trend continues, the temperature in 2030 will be 1°C higher than the temperature in 2029. (False)
- The average increase in temperature each year is 1°C. (False)
- The average increase in temperature every 5 years is 1°C. (True)
True Statements:
- y = 0.2x + 15 represents the linear equation.
- In the year 2010 the temperature was 17 °C.
- The average increase in temperature every 5 years is 1°C.
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