CHAPTER SUMMARY
An algebraic expression combines numbers, variables, and
operation symbols. For example, 2×2
+ 5xy – 3y2
is an algebraic
expression in the variables x and y. 2×2
, 5xy and – 3y2
are the
terms of the algebraic expression, and the numbers 2, 5 and – 3
are coefficients of the terms.
Univariate Polynomials are algebraic expressions in one
variable. Thus x2
+ 5x + 3 and 3y3
– 4y2
+ 5 are univariate
polynomials in x and y, respectively. The highest power of the
variable in a univariate polynomial is called its degree. Thus,
x2
+ 5x + 3 is of degree 2 while 3y3
– 4y2
+ 5 is of degree 3.
A polynomial of degree one is called a linear polynomial. Hence,
2x + 3 and 5 – 4y are linear polynomials in the variables x and y,
respectively.
Linear growth refers to a pattern in which a quantity increases
by a fixed amount over equal intervals. In contrast, linear decay
describes a pattern in which a quantity decreases by a fixed
amount over equal intervals.
A linear pattern is a sequence of numbers where the difference
between consecutive terms is constant.
z A linear relationship between two variables x and y is
represented by a straight line y = ax + b. The slope of this line is
a. The constant b is called the y-intercept which is the distance
from the origin where the line cuts the y-axis. When b = 0, the
equation of the line becomes y = ax and the line passes through
the origin.
z Linear growth is represented by a straight line with positive
slope and linear decay is represented by a straight line with
negative slope.
z Parallel lines are of the form y = ax + b, where the slope a is fixed
while b, the y-intercept, varies.