linear equation

Question

In 1990, the cost of tuition at a large Midwestern university was $93 per credit hour. In 1999, tuition had risen to $210 per credit hour.

Determine a linear equation  to represent the cost of tuition in terms of , the number of years since 1990.

In the year 2003, tuition will be $ ________per credit hour.

In the year ____________, tuition will be $301 per credit hour

Answer 1

Let T = cost per credit hour and Y = year.

When Y = 1990 T = $93

When Y = 1999 T = $210

Since the change is assumed to be linear, the slope is ($210 - $93) / (1999 - 1990) = $117/9 = $13/year

T = $93 + $13*(Y-1990)

When Y = 2003, T = $93 + $13(2003-1990) = $262

Recall the change T is assumed to be linear over Y.

In 1999, T was given as $210. The slope, m = $13/year.

$310 - $210 = $91. Since m = $13/year, $91/$13 = 7 years have passed since 1999.

When T = $301, Y = 2006.

As a check, notice that in 2003 T was found to be $262, and 301-262 = 39 and 39/13 = 3 more years. 2003 + 3 = 2006