The linear equation represented on the coordinate plane shows the average temperature increase in a city since the year 2000

Question

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.
The average increase in temperature every 5 years is 1°C.
Question 2
2.

Answer 1

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.

1. 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.

2. 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.

3. 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.

4. 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:

1. y = 0.2x + 15 represents the linear equation.
2. In the year 2010 the temperature was 17 °C.
3. The average increase in temperature every 5 years is 1°C.