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 + 46. 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? (b) what is the temperature on the surface of the planet?

Explanation:

Step1: Analyze the slope for temperature - change

The equation is in the form $y = mx + b$ (slope - intercept form), where $m$ is the slope. For $y=-3x + 46$, the slope $m=-3$. The slope represents the change in $y$ (temperature) for a unit - change in $x$ (height). So, for each kilometer increase in height ($x$), the temperature ($y$) changes by $- 3^{\circ}C$.

Step2: Find the surface temperature

The surface of the planet corresponds to $x = 0$. Substitute $x = 0$ into the equation $y=-3x + 46$. Then $y=-3\times0 + 46=46$.

Answer:

(a) $-3$
(b) $46$