Question

The cost of K-12 education per student was $2200 in 1978 and increased to $10,300 in 2008. (Source: Department of Education). (a) Find a linear equation that models these data. Let C represent the cost per student and x represent the number of years after 1978.

Answer 1

Answer: $C=270x+2200$

Step-by-step explanation:

Given

Cost per student in the year 1978 is $2200

The cost increases to $10,300 in 2008

Suppose $C=mx+a$ is the linear equation defining the cost per student after x years

Substitute the value for 1978

$\Rightarrow 2200=m(0)+c\\\Rightarrow c=2200$

After 30 years it becomes

$\Rightarrow 10,300=m(30)+2200\\\Rightarrow 30m=8100\\\Rightarrow m=270$

Thus, the linear equation becomes

$\Rightarrow C=270x+2200$