Recent studies indicate that the average surface temp. of the earth has been rising steadily. Some scientists have modeled the temp. by the linear function T= 0.02t + 8.50, where T is temp. in degrees Celsius and t represents years since 1900.

What do the slope and T-intercept represent?

I am not sure if I am overthinking this problem and if it is as simple as the T-intercept represents the temp. in deg. C and the slope represents the average surface temp. of the earth in various years?

slope represents rate of change of temp

intercept is the temp in the year 1990

Ok so here's a similar problem.

The manager of a weekend flea market knows from past experience that if he charges x dollars for a rental space at the market, then the number y of spaces he can rent is given by the equation y= 200-4x.

Is this correct?
Slope represents the relationship between amount charged per space and how many spaces he will rent. The more he charges, the less he will rent.

y-intercept represents the # of spaces he can rent

x-intercept represents the amount of money he can make or charge

You're on the right track! In the linear function T = 0.02t + 8.50, the slope and T-intercept each have specific meanings.

The slope, represented by 0.02, indicates the rate at which the average surface temperature of the Earth is changing with respect to time. In this case, the slope value suggests that for every year that passes since 1900, the temperature would increase by 0.02 degrees Celsius on average. This implies a steady, gradual temperature increase over time.

The T-intercept, represented by 8.50, refers to the value of the temperature (in degrees Celsius) at the starting point of the timeline, which is the year 1900 in this case. It represents the approximate average surface temperature of the Earth in that specific year.

So, to summarize, the slope represents the rate of change of temperature over time, while the T-intercept represents the initial temperature at the starting point of the timeline.