Everyone knows what a line is, but providing a rigorous definition
proves to be a challenge.
A line with slope m
through a point P = (a,b) is the set of all points (x,y)
- b)/(x - a) = k.
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
| Slope Intercept
Equation of a Line
y - y1 = m(x - x1)
Piecewise Linear Functions
A function is piecewise linear if it is made up of parts of lines
|f (x) =
|x + 4
||x < -2
|2x - 1
||-2 < x < 1
||1 < x
We graph this line by sketching the appropriate parts of each line on the same
Suppose you own a hotel that has 150 rooms. At $80 per room, you have
140 rooms occupied and for every $5 increase in price you expect to have two
additional vacancies. Come up with an equation that gives rooms
occupied as a function of price.
Let x be the price of a
room and y be the number of rooms occupied. Then we have an equation
of a line that passes through the point (80,140) and has slope -1/5.
Hence the equation is:
y - 140 = -1/5 (x - 80)
y = -1/5 x + 16 + 140
y = -1/5 x
What should you do if your two year old daughter has a 40 degree
Hint: We have the two points: (0,32) and (100,212)
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
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?
Wasabi restaurant must pay either a flat rate of $400 for rent or 5% of the
revenue, whichever is larger. Come up with the equation of the function
that relates rent as a function of revenue.
Math 103A Home Page
Back to the Math Department
e-mail Questions and