4. the graph to the right shows the temperature in a room where the heater was turned on. what does the…

Brief Explanations:

The equation of a line is (y = mx + b), where (m) is the slope and (b) is the (y -)intercept. In the context of a temperature - time graph ((y) represents temperature and (x) represents time):

• The slope (m=\frac{\Delta y}{\Delta x}). Here, (\Delta y) is the change in temperature and (\Delta x) is the change in time. So, the slope represents the rate of change of temperature with respect to time. That is, how many degrees Fahrenheit the temperature increases per hour.
• The (y -)intercept occurs when (x = 0). In the context of the temperature - time graph, when (x = 0) (at the start, when the heater is just turned on), (y=b). So, the (y -)intercept represents the initial temperature of the room (the temperature when the heater was first turned on).

Answer:

The slope represents the rate at which the temperature increases per hour. The (y -)intercept represents the initial temperature of the room when the heater was turned on.