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The problem presented involves creating a mathematical equation based on a scenario where scientists are studying the temperature on a distant planet. Here is the breakdown of the information provided and how to create the equation:

1. **Given Information:**
   - The surface temperature on the planet (at \( H = 0 \), where \( H \) is the height above the surface in kilometers) is \( 30^\circ \) Celsius.
   - The temperature decreases by \( 3^\circ \) Celsius for each kilometer you go up from the surface.

2. **Define Variables:**
   - Let \( T \) represent the temperature (in Celsius) at height \( H \) kilometers above the surface.
   - \( H \) is the height in kilometers.

3. **Creating the Equation:**
   - Since the temperature decreases linearly with height, we can use a linear equation to model this situation.
   - The rate of change (slope) of the temperature with respect to height is \( -3 \) (since temperature decreases by \( 3^\circ \) per kilometer).
   - The initial value (y-intercept) is \( 30 \) (the temperature at \( H = 0 \)).

   Using the slope-intercept form of a line \( T = mH + b \), where \( m \) is the slope and \( b \) is the y-intercept, we get:

   \[
   T = -3H + 30
   \]

4. **Final Equation:**
   - The equation that models the temperature \( T \) in terms of the height \( H \) is:
     \[
     T = -3H + 30
     \]

This equation indicates that for every 1 kilometer increase in height (\( H \)), the temperature \( T \) decreases by 3 degrees Celsius.

Would you like me to go over the process in more detail or provide guidance on graphing this equation?

### Related Questions
1. What would the temperature be at a height of 5 kilometers?
2. How would the equation change if the temperature decreased by 5 degrees per kilometer instead?
3. Can you explain why this is a linear relationship rather than a different type of function?
4. How would you determine the height at which the temperature reaches 0 degrees Celsius?
5. What would the equation look like if the initial temperature at the surface was different, say 40 degrees Celsius?

### Tip
When creating linear equations based on word problems, identifying the initial value and rate of change can quickly help set up the equation in slope-intercept form.

Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is 30 degrees Celsius. They also find that the temperature decreases by 3 degrees Celsius for each kilometer you go up from the surface. Let T represent the temperature (in Celsius), and let H be the height above the surface (in kilometers). Write an equation relating T to H, and then graph your equation.

Learn how to create a linear equation that models temperature changes with height on a distant planet. The surface temperature is 30 degrees Celsius, decreasing by 3 degrees Celsius per kilometer. Suitable for Grades 8-10 students, this problem covers linear equations and slope-intercept form.

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