Scientists are studying the temperature on a distant planet. Let

y

represent the temperature (in degrees Celsius). Let

x

represent the height above the surface (in kilometers). Suppose that

x

and

y

are related by the equation

y=41-3x

.

Answer the questions below.

Note that a change can be an increase or a decrease.

For an increase, use a positive number. For a decrease, use a negative number.

what is the temperature on the surface of the planet?

what is the temperature change for each kilometer we go up from the surface?

Now, the temperature on the surface can be find when the height above the surface is zero, that is \(x=0\). So, we replace this value and solve for \(y\)

\(y=41-3x=41-3(0)\\y=41\)

Therefore, the temperature on the surface of the planet is 41 °C.

The second question is about the constant rate of change of the given relation, which is also the slope of the linear expression. That constant rate of change is always the coefficient of variable \(x\). Therefore, the ratio of change is \(r=-3\). Which means the tempearture decreases 3 °C when the height increases 1 km.

The decreasing behaviour is deduct from the ratio of change, when it's negative, that means the function decreases, like in this case.