Lines

I.  Midterm I

II.  Lines (definitions)

Students will pair up to give the definition of a line.  

Definition:  A line with slope m through a point P = (a,b) is the set of all points (x,y) such that (y - b)/(x - a) = k.

III.  The Slope Intercept Form of the equation of a Line

Given a point (x₁,y₁) and a slope m, the equation of the line is

y - y₁ = m(x - x₁)  

 Piecewise Linear Functions

A function is piecewise linear if it is made up of parts of lines

Example

f(x) =  

x + 4	x < 2
2x - 1	-2 < x < 1
3x	1 < x

We will use the TI 85 calculator to sketch this graph.

VI.  Applications

A)  What should you do if your two year old daughter has a 40 degree C temperature?

Hint:  We have the two points:  (0,32) and (100,212)

B)  Suppose that your company earned $30,000 five years ago and $35,000 three years ago.  Assuming a linear growth model, how much will it earn this year?

C)  My rental was bought for $204,000 three years ago.  Depreciation is set so that the house depreciates linearly to zero in twenty years from the purchase of the house.  If I plan to sell the house in twelve years for $250,000 and capital gains taxes are 28% of the difference between the purchase price and the depreciated value, what will my taxes be?