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

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 y-axis and x-intercept where it crosses the x-axis)

For an equation Ax + By = C, A ¹ 0 or B ¹ 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

Slope of a line -

Where P is (x1, y1), Q (x2, y2), x1 ¹ x2 .

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

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

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DOUGLAS A. WILLIAMS, ARIZONA STATE UNIVERSITY, DEPARTMENT OF MATHEMATICS