Question

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 using the axes below.

Answer 1

If the temperature drops by 3 degrees for every kilometer then that would be your slope, -3. Since 30 is the temperature at the surface then let that be your y-intercept. A line is y=mx+b, let m=-3, x=H, y=T, and b=30. So the equation would be T= -3H+30

Answer 2

The required equation is
`T=30-3H`.

Explanation:

It is given that the surface temperature at one location is 30 degrees Celsius and the temperature decreases by 3 degrees Celsius for each kilometer you go up from the surface.

Total temperature = Initial temperature + Change in temperature

Let T represent the temperature (in Celsius), and let H be the height above the surface (in kilometers).

The temperature T on a distant planet at the height H km above the surface is defined by the equation

`T=30+(-3)H`

`T=30-3H`

Therefore, the required equation is
`T=30-3H`.

The table of values is

H T

0 30

10 0

Plot these ordered pairs on the coordinate plane and connect them by a straight line.