Question3. An arctic cold front is moving through an area. It is when the temperature begins to drop. The scatter plot suggests a linear relationship between the temperature and the number of hours since the cold front arrived.
a. What does the rate of change, or slope, represent in this situation?
b. What is the -intercept for the trend line and what does it represent?
37 Tempature ( )
c. What equation relates the change in temperature, to the number of hours after the cold front arrives, ?
Temperature After Cold Eront
Use and to find slope.
Studdy Solution
STEP 1
1. The temperature decreases linearly over time due to the cold front.
2. The initial temperature is Fahrenheit.
3. The slope of the line is , indicating the rate of temperature change per hour.
4. The -intercept is , representing the initial temperature when .
STEP 2
1. Interpret the slope and its significance.
2. Determine the -intercept and its significance.
3. Formulate the equation of the line using the slope and -intercept.
STEP 3
The slope, , represents the rate of temperature change per hour. Specifically, it indicates that the temperature decreases by Fahrenheit for every hour that passes after the cold front arrives.
STEP 4
The -intercept is . This represents the initial temperature of Fahrenheit at the moment the cold front arrives, which is when .
STEP 5
Using the slope-intercept form of a linear equation, , where is the slope and is the -intercept, we can write the equation for the temperature change as:
This equation relates the temperature to the number of hours after the cold front arrives.
The equation that relates the change in temperature to the number of hours after the cold front arrives is:
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