Questions: Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is 35 degrees Celsius. They also find that the temperature decreases by 5 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 using the axes below. Equation: = (A) x 5

Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is 35 degrees Celsius. They also find that the temperature decreases by 5 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 using the axes below.

Equation:

=

(A)

x

5

Transcript text: Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is $35^{\circ}$ Celsius. They also find that the temperature decreases by $5^{\circ}$ 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 using the axes below. Equation: $\square$ $\square=$ $\square$ $\square$ (A) $\qquad$ \[ x \] $\square$ 5

Solution

Solution Steps

Step 1: Determine the relationship between temperature and height.

The temperature at the surface (H=0) is 35°C. The temperature decreases by 5°C for every kilometer above the surface. This represents a linear relationship.

Step 2: Write the equation.

The equation relating T to H is: T = 35 - 5H

Step 3: Identify two points for graphing.

When H = 0, T = 35. This gives the point (0, 35). When H = 1, T = 35 - 5(1) = 30. This gives the point (1, 30).

Final Answer

Equation: T = 35 - 5H

Graph: A line segment connecting the points (0, 35) and (1,30) on the given axes would represent the relationship. Since height cannot be negative, the graph would only exist for non-negative values of H. Additional points can be plotted by choosing different values for H such as 2, 3, 4, and so on, and solving for T in each case.

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