Let's analyze the linear equation given:
\[ y = 0.2x + 15 \]
In this equation:
- \( y \) represents the average temperature in degrees Celsius.
- \( x \) represents the number of years since 2000.
From this, we can derive the following truths about the statements given:
-
y = 0.2x + 15 represents the linear equation:
- True. This is the equation provided.
-
The average increase in temperature each year is 1°C:
- False. The slope of the equation is 0.2, which means the temperature increases by 0.2°C each year, not 1°C.
-
In the year 2010 the temperature was 17 ° C:
- Calculate \( x \) for the year 2010: \( x = 2010 - 2000 = 10 \).
- Substitute \( x \) into the equation: \( y = 0.2(10) + 15 = 2 + 15 = 17°C \).
- True. Therefore, the temperature in 2010 was indeed 17°C.
-
If the trend continues, the temperature in 2030 will be 1°C higher than the temperature in 2029:
- Calculate \( x \) for 2030: \( x = 2030 - 2000 = 30 \) and for 2029: \( x = 2029 - 2000 = 29 \).
- The difference in temperature between 2030 and 2029 will be \( y(30) - y(29) = (0.2(30) + 15) - (0.2(29) + 15) = 0.2 \), which is 0.2°C.
- False. The temperature in 2030 will be 0.2°C higher than in 2029, not 1°C.
-
The average increase in temperature every 5 years is 1°C:
- Over 5 years, \( y \) changes by \( 0.2 \times 5 = 1°C \).
- True. The increase in temperature every 5 years is indeed 1°C.
Summary of 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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