Mathematics

Thinking Mathematically

7th Edition

You are required to purchase the access code for MyLab/Mastering (MyMathLab).

Thinking Mathematically – eText (w/Access Code – MyMathLab ) – ISBN # 9780134705095

ANSWER

Algebra: Equations, Inequalities, Graphs

1. Plotting an ordered pair (x,y)

An ordered pair (x,y) is essential in plotting because the coordinates of a point that is in the coordinate system are contained in the ordered pair. The pair has two numbers where the first number corresponds to the x-coordinate while the second number corresponds to the y-axis. For instance in the pair (4,9), 4 corresponds to the x-axis and 9 corresponds to the y-axis. To plot a point, you draw a dot at the coordinates that correspond to the ordered pair and then project the points using straight line, where lines intersect is the point represented by the ordered pair. Example,

y-axis  9 .

x-axis

4

1. Checking if an ordered pair is a solution of an equation

An ordered pair, say (x,y), can be used to solve an equation that is expressed in form of x and y. thus, to check if the ordered pair is a solution of the equation, identify the value of the ordered pair that corresponds to the x-value and plug it into equation. Then simplify to check if the y-value in the equation is equivalent to the corresponding y-value in the ordered pair. If the values are same, then the ordered pair is a solution of the equation otherwise it is not. For instance, in the equation, y = 2x+1, the ordered pair (0,1) is a solution since plucking 0 in the x-value of the equation gives y=2*(0)+1 = 1. The ordered pair (2,3) is not a solution because plucking 2 in the x-value of the equation results in y=2*(2)+1 = 5.

• Slope of “0”

A slope results from the change in y divided by the corresponding change in x. A slope of “0” implies that the plotted line will be a horizontal line. For instance, an equation in the form of y=mx+b where m is the slobe, x is the corresponding x-value in the ordered pair and b is a constant value such that y = m*3 + 2. Plucking slope of 0 in the equation gives y=0*3 + 2 and simplifies as y = 0+2, y=2

Plotting this gives a horizontal line along the value y=2

y-axis

2                         y=2

x-axis

1. Undefined slope

It is an infinitely large slope and represents a vertical line. For the undefined slope, the x-coordinate does to change for different values of y-coordinate. An example of ordered pairs that result in an undefined slope is (3,1) and (3,6).

This is illustrated below.

y-axis

6

1      3                x-axis