Linear Equations
Let's glance at an example:
The initial cost for setting up a new helipad is estimated to be 50 thousand dollars. The maintenance cost for the helipad increases with the number of helicopters using it. So if the number of helicopters using the helipad is H and the maintenance cost per helicopter is 2.5 thousands dollars per month, the total amount spent on this project at the end of the first month is estimated to be
C = 2.5 H + 50
where C is the cost in thousands of dollars spent.
If the amount allotted for this project for the first month is equal to 100 thousand dollars (including the set up cost), how many helicopters can be allowed to use the helipad during the first month?
Let's consider a solution:
The total cost is equal to the sum of the setup cost plus the
maintenance cost.
2.5 H + 50 = 100
Using the properties we learned, we can solve the equation as follows:
2.5 H + 50 - 50 = 100 - 50
2.5 H = 50
(2.5/2.5) H = 50 / 2.5
H = 20
So the number of helicopters allowed during the first month is 20.
A few simple facts that you should know
Did you know that the above example is a linear equation?
A Linear Equation is an equation of the form
m * X + c = 0 where X is the unknown.
The name "linear" stems from the fact that the graph of this equation is a straight line. If we plot a graph of mx + c we will see a straight line with a slope of m that intersects the y axis at y = c. Solving the equation means finding the value of x where the line intersects the x-axis.
Do you want to see how the graph for the equation 2.5x - 50 will look?
Graphing interactive workbench