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MAT 119 FALL 2001
MAT 119
FINITE MATHEMATICS
NOTES
PART 1 – LINEAR ALGEBRA
CHAPTER 1
LINEAR EQUATIONS
1.1
Rectangular Coordinates; Lines
x-axis – horizontal axis
y-axis – vertical axis
origin O – intersection of the two axes
rectangular (Cartesian) coordinate system –
xy-plane – plane containing both axes
coordinate axes – x-axis and y-axis
ordered pair (x, y) – coordinates of a point P
x – x-coordinate or abscissa
y – y-coordinate or ordinate
plot – dot that marks a point
quadrants – the four sections that the two axes divides the xy-plane into
DOUGLAS A. WILLIAMS, ARIZONA STATE UNIVERSITY, DEPARTMENT OF MATHEMATICS
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MAT 119 FALL 2001
Graphs of Linear Equations in Two Variables
Ax + By = C (general equation of a line)
Graph of equation – set of all points (x, y) whose coordinates satisfy the equation
Intercepts – points where the line crosses the axes (y-intercept where it crosses the yaxis and x-intercept where it crosses the x-axis)
For an equation Ax + By = C, A  0 or B  0,
Set y = 0 and solving for x gives the x-intercept, and
Set x = 0 and solving for y gives the y-intercept
Equation of a vertical line – x = a (a, 0) is the x-intercept
Equation of a horizontal line – y = b
(0, b) is the y-intercept
y 2  y1
x 2  x1
Where P is (x1, y1), Q (x2, y2), x1  x2 .
Slope of a line -
m
Point-Slope Form of an equation of a line
(x1, y1) and slope m
y – y1 = m(x – x1)
Slope-Intercept form of an equation of a line
(0, b) and slope m
y = mx + b
DOUGLAS A. WILLIAMS, ARIZONA STATE UNIVERSITY, DEPARTMENT OF MATHEMATICS
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MAT 119 FALL 2001
1.2
Parallel and Intersecting lines
Coincident Lines
Coincident lines that are vertical have undefined slope and the same x-intercept.
Coincident lines that are non-vertical have same slope and the same intercepts.
Parallel lines
Parallel lines that are vertical have undefined slope and different x-intercepts.
Parallel lines that are non-vertical have same slope and different x-intercepts.
Intersecting lines – have different slopes
Perpendicular lines
Two distinct non-vertical lines L and M with slopes m1 and m2, respectively, are
perpendicular if and only if m1m2 = -1. (the product of their slopes = -1)
1.3
Applications
Finding linear equation model and do predictions
Use of cost and revenue equations to find break-even points and profit/loss
Mixture problems
Supply/demand equations
DOUGLAS A. WILLIAMS, ARIZONA STATE UNIVERSITY, DEPARTMENT OF MATHEMATICS
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