In 2002 a camp had 500 campers. Five years later the camp had 1000 campers. Write a linear equation to represent the camp.

Answer 1

500 campers is the starting point in 2002, so 500 is the y intercept, also known as variable b.

The year 2002 would become a 0 value on the x axis.

Over 5 years, the campers increase by 500, so the rate of increase is 500 divided by 5, or 100, so slope m is 100.

The equation becomes y = mx + b = 100x + 500

Answer 2

It's more likely we'll be asked for the number of campers given a particular year, so we'll use an ordered pair (x,y) to represent (year, campers), we know we have the points (2002, 500) and (2002+5, 1000) = (2007, 1000). Using the formula for slope m = (y_2 - y_1) / (x_2 - x_1), we have m = (2007-2002) / (1000-500) = 1/100. Use the formula again, but we'll replace m and only one x-y pair: 1/100 = (y - 2002) / (x - 500).