As we learned in the last topic on graphing linear functions, slope is not simply a creation of algebra or geometry: slope is a concept that impacts the real world around us.

Consider the graph above, representing an annual income of $3,000 during the first year, which increases by $2,000 each year thereafter. This constant rate of change is understood algebraically as slope, and the relationship of the data establishes a linear function (y = 2000x +1000), with x being the number of full years of work. Further, assuming the rate of change will remain unchanged, we can predict confidently that after working 10 years (x = 10), the income will be $23,000:

A large cattle rancher desires to gradually reduce the size his herd over the next 15 years.  He now has 40,000 steer, and has determined that a reduction in the herd size of 2,000 steer per year would be best. Is this a linear function?  Why? What is the equation of the linear function? How many steer will be in the herd at the end of the 7th year? Click Here to check your solution.