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Since points and ordered pairs are so closely related, the two terms are sometimes used interchangeably. The following two phrases have the same meaning:
Plot the ordered pair $(2,\text{\hspace{0.17em}}6)$ .
We begin at the origin. The first number in the ordered pair, 2, tells us we move 2 units to the right (
$+2$ means 2 units to the right) The second number in the ordered pair, 6, tells us we move 6 units up (
$+6$ means 6 units up).
Plot the ordered pairs.
$(1,\text{\hspace{0.17em}}3),\text{\hspace{0.17em}}(4,\text{\hspace{0.17em}}-5),\text{\hspace{0.17em}}(0,\text{\hspace{0.17em}}1),\text{\hspace{0.17em}}(-4,\text{\hspace{0.17em}}0)$ .
(Notice that the dotted lines on the graph are only for illustration and should not be included when plotting points.)
Plot the following ordered pairs. (Do not draw the arrows as in Practice Set A.)
$(8,\text{\hspace{0.17em}}2),\text{\hspace{0.17em}}(10,\text{\hspace{0.17em}}-3),\text{\hspace{0.17em}}(-3,\text{\hspace{0.17em}}10),\text{\hspace{0.17em}}(0,\text{\hspace{0.17em}}5),\text{\hspace{0.17em}}(5,\text{\hspace{0.17em}}0),\text{\hspace{0.17em}}(0,\text{\hspace{0.17em}}0),\text{\hspace{0.17em}}\left(-7,\text{\hspace{0.17em}}-\frac{3}{2}\right)$ .
As accurately as possible, state the coordinates of the points that have been plotted on the following graph.
Using ordered pair notation, what are the coordinates of the origin?
$\text{Coordinates\hspace{0.17em}of\hspace{0.17em}the\hspace{0.17em}origin\hspace{0.17em}are}\left(0,0\right)$ .
We know that solutions to linear equations in two variables can be expressed as ordered pairs. Hence, the solutions can be represented as points in the plane. Consider the linear equation $y=2x-1$ . Find at least ten solutions to this equation by choosing $x\text{-values}$ between $-4$ and 5 and computing the corresponding $y\text{-values}$ . Plot these solutions on the coordinate system below. Fill in the table to help you keep track of the ordered pairs.
$x$ | ||||||||||||
$y$ |
Consider the
$xy\text{-plane}$ .
Complete the table by writing the appropriate inequalities.
I | II | III | IV |
$x>0$ | $x<0$ | $x$ | $x$ |
$y>0$ | $y$ | $y$ | $y$ |
I | II | III | IV |
$x>0$ | $x<0$ | $x<0$ | $x>0$ |
$y>0$ | $y>0$ | $y<0$ | $y<0$ |
A psychologist, studying the effects of a placebo on assembly line workers at a particular industrial
site, noted the time it took to assemble a certain item before the subject was given the placebo,
$x$ , and the time it took to assemble a similar item after the subject was given the placebo,
$y$ . The psychologist's data are
$x$ | $y$ |
10 | 8 |
12 | 9 |
11 | 9 |
10 | 7 |
14 | 11 |
15 | 12 |
13 | 10 |
The following data were obtained in an engineer’s study of the relationship between the amount of pressure used to form a piece of machinery,
$x$ , and the number of defective pieces of machinery produced,
$y$ .
$x$ | $y$ |
50 | 0 |
60 | 1 |
65 | 2 |
70 | 3 |
80 | 4 |
70 | 5 |
90 | 5 |
100 | 5 |
Yes, there does appear to be a relation.
The following data represent the number of work days missed per year,
$x$ , by the employees of an insurance company and the number of minutes they arrive late from lunch,
$y$ .
$x$ | $y$ |
1 | 3 |
6 | 4 |
2 | 2 |
2 | 3 |
3 | 1 |
1 | 4 |
4 | 4 |
6 | 3 |
5 | 2 |
6 | 1 |
A manufacturer of dental equipment has the following data on the unit cost (in dollars),
$y$ , of a particular item and the number of units,
$x$ , manufactured for each order.
$x$ | $y$ |
1 | 85 |
3 | 92 |
5 | 99 |
3 | 91 |
4 | 100 |
1 | 87 |
6 | 105 |
8 | 111 |
8 | 114 |
Yes, there does appear to be a relation.
( [link] ) Simplify ${\left(\frac{18{x}^{5}{y}^{6}}{9{x}^{2}{y}^{4}}\right)}^{5}$ .
(
[link] ) Supply the missing word. An
equation
( [link] ) Simplify the expression $5xy(xy-2x+3y)-2xy(3xy-4x)-15x{y}^{2}$ .
( [link] ) Identify the equation $x+2=x+1$ as an identity, a contradiction, or a conditional equation.
contradiction
(
[link] ) Supply the missing phrase. A system of axes constructed for graphing an equation is called a
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