Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 18, 2024

Scientists study distant planet's temperature $y$ (°C) and height $x$ (km). The equation is $-7x + 38 = y$ . What is the temperature change per kilometer?

STEP 1

Assumptions
1. The temperature on the distant planet is represented by $y$ in degrees Celsius.
2. The height above the surface is represented by $x$ in kilometers.
3. The relationship between $x$ and $y$ is given by the linear equation $-7x + 38 = y$ .

STEP 2

The equation $-7x + 38 = y$ describes a linear relationship between the height above the surface ( $x$ ) and the temperature ( $y$ ). The coefficient of $x$ represents the rate of change of temperature with respect to height.

STEP 3

To find the temperature change for each kilometer we go up from the surface, we need to look at the coefficient of $x$ in the equation.

STEP 4

The coefficient of $x$ is $-7$ , which means that for each kilometer increase in height ( $x$ ), the temperature ( $y$ ) decreases by 7 degrees Celsius.

STEP 5

Therefore, the temperature change for each kilometer we go up from the surface is a decrease of 7 degrees Celsius.
The temperature decreases by 7 degrees Celsius for each kilometer increase in height.

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