Question

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 = -3x + 21. 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. (a) what is the temperature change for each kilometer we go up from the surface? \\(\square\\) °c (b) what is the temperature on the surface of the planet? \\(\square\\) °c

Explanation:

Step1: Analyze the linear equation

The equation is \( y = -3x + 21 \), which is in the slope - intercept form \( y=mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value when \( x = 0 \)).

Step2: Find the temperature change per kilometer (part a)

In the equation \( y=-3x + 21 \), the coefficient of \( x \) is \( - 3 \). This coefficient represents the rate of change of \( y \) with respect to \( x \). So, for each kilometer we go up (increase in \( x \) by 1), the temperature \( y \) changes by \( - 3^{\circ}\text{C} \).

Step3: Find the surface temperature (part b)

The surface of the planet is at \( x = 0 \) (height above surface is 0). Substitute \( x = 0 \) into the equation \( y=-3x + 21 \). We get \( y=-3(0)+21=21 \). So the temperature on the surface is \( 21^{\circ}\text{C} \).

Answer:

s:
(a) \(-3\)
(b) \(21\)