Question

1. The linear equation represented on the coordinate plane shows the average temperature increase in a city since the year 2000 Select all the statements that are true for the linear equation. (3 points) Responses y = 0.2x + 15 represents the linear equation y = 0.2x + 15 represents the linear equation The average increase in temperature each year is 1°C. The average increase in temperature each year is 1°C. In the year 2010 the temperature was 17 ° C. In the year 2010 the temperature was 17 ° C. If the trend continues, the temperature in 2030 will be 1°C higher than the temperature in 2029 If the trend continues, the temperature in 2030 will be 1°C higher than the temperature in 2029 The average increase in temperature every 5 years is 1°C.

Answer 1

To analyze the linear equation \( y = 0.2x + 15 \), we need to understand what each component represents:

1. **Identifying the terms**:
- \(y\) represents the average temperature in degrees Celsius.
- \(x\) represents the number of years since 2000. Therefore, if \(x = 0\), it represents the year 2000, if \(x = 1\), it’s 2001, and so on.

2. **Slope Analysis**:
- The coefficient of \(x\) (which is \(0.2\)) represents the rate of change in temperature per year. Thus, the average increase in temperature each year is **0.2°C**, not **1°C**.

3. **Finding temperature in the year 2010**:
- For the year 2010, \(x = 2010 - 2000 = 10\).
- Plugging \(10\) into the equation:
\[
y = 0.2(10) + 15 = 2 + 15 = 17°C.
\]
- Therefore, it is correct that in the year 2010 the temperature was **17°C**.

4. **Predicting temperature in 2030**:
- For the year 2030, \(x = 2030 - 2000 = 30\).
- In 2029, \(x = 29\):
\[
y_{2029} = 0.2(29) + 15 = 5.8 + 15 = 20.8°C.
\]
- In 2030:
\[
y_{2030} = 0.2(30) + 15 = 6 + 15 = 21°C.
\]
- Thus, the temperature in 2030 will indeed be **0.2°C higher than the temperature in 2029**, not **1°C higher**.

5. **Average increase every 5 years**:
- The average increase in temperature over 5 years (from \(x\) to \(x + 5\)):
\[
\text{Increase} = y(x + 5) - y(x) = [0.2(x + 5) + 15] - [0.2x + 15] = 0.2x + 1 - 0.2x = 1°C.
\]
- Thus, the average increase in temperature every **5 years is 1°C**.

### Summary:
Taking all this into account, the true statements from the options given are:

1. **True**: "In the year 2010 the temperature was 17 °C."
2. **True**: "If the trend continues, the temperature in 2030 will be 0.2°C higher than the temperature in 2029." (Note: this statement as it is written about 1°C is false.)
3. **True**: "The average increase in temperature every 5 years is 1°C."

The incorrect statements are regarding the average annual temperature increase (which is 0.2°C) and the temperature difference between 2030 and 2029 (which is also 0.2°C).