©Zarestky
Math 141 Week in Review
Texas A&M University
Week 1 Key Topics
Sections 1.1-1.2
•
•
•
•
•
"y y 2 # y1 rise
=
=
"x x 2 # x1 run
o The slope measures the rate of change of y with respect to x.
o A horizontal line has a slope of 0.
o A vertical line has undefined slope.
! are parallel if the slopes are equal, i.e., m = m
Two lines
1
2
Two lines are perpendicular if the product of the slopes is −1, i.e. m1 ! m2 = "1
Find intercepts.
o x-intercept
 Where the line crosses the x-axis
 Set y = 0 and solve.
o y-intercept
 Where the line crosses the y-axis
 Set x = 0 and solve.
Write equations of lines.
o
Point-Slope Form: y ! y1 = m ( x ! x1 )
o
Slope-Intercept Form: y = mx + b
o
General form of a line: Ax + By + C = 0 , A and B not both equal to 0.
o
Vertical line through (a, b) is x = a.
o
Horizontal line through (a, b) is y = b.
Calculate slope: m =
!
Section 1.3
•
•
•
Linear Depreciation: value, V, as a function of time, t
Linear Cost, Revenue, and Profit
o
C(x) = cx + F gives the total cost of producing x items where F represents
the fixed costs and slope c represents the production cost per unit.
o
R(x) = sx gives the revenue from the sale of x items where s is the price
per unit.
o
P(x) = R(x) – C(x) gives the profit from producing and selling x items.
Supply and Demand
o
Price as a function of quantity, (x, p)
o
Demand has negative slope.
o
Supply has positive slope.
©Zarestky
Math 141 Week in Review
Texas A&M University
Section 1.4
•
Break-Even Analysis
o
Cost equals revenue. Find the point of intersection.
 Break-even quantity and $.
o
Profit equals 0. Find the x-intercept.
•
Equilibrium Point
o
Supply equals demand. Find the point of intersection.
o
The intersection point is ( x0 , p0 ) .
 x0 is the equilibrium quantity
 p0 is the equilibrium price