The equation y=58−x represents the temperature, y, in degrees fahrenheit and the time, x, in hours from 6 p. m. to 9 a. m. on a certain day. let x = 0 represent the temperature at 6 p. m. what is the average rate of change in temperature from 6 p. m. to 9 a. m.?

From the equation, y=58-x, where y is temperature and x is time in hours.
Time from 6 p.m to 9 a.m = 15 hours
Therefore, the value of y= 58 - 15 =  43 fahrenheits
The average rate of change in temperature = temperature divided by time
       = 43 / 15 =2.86 Fahrenheit/hour
Therefore, the rate of change in temperature will be given by 2.86 Fahrenheit /hour.