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Algebra 1 > Chapter 3A > Flashcards

Chapter 3A Flashcards

1
Q

A type of graph (or a simulation of bars) arranged either vertically or horizontally to show comparisons of data

A

Bar graph

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1
Q

An organized way of displaying ordered pairs

A

Tables of values

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2
Q

What is the definition of a linear equation in one variable.

A

An equation that can be written as Ax+B=C Where A,B, and C are real numbers. With A ≠ 0

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3
Q

A pair of numbers written in parentheses in which the order of the numbers is important. (-2,7)

A

Ordered pair

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5
Q

A type of graph used to show changes, or trends in data overtime.

A

Line graph

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5
Q

What is the definition of a linear equation in two variables.

A

An equation that can be written as Ax+By=C Where A,B, and C are real numbers. With neither A nor B ≠ 0

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6
Q

An ordered pair that is the solution of an equation is said to “______” the equation

A

Satisfy

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8
Q

When reading an ordered pair the first value is always ___and___ is the second value.

A

X Y

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8
Q

When reading ordered pairs (2,13) and (13,2) are considered ________

A

Not the same.

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9
Q

Ordered pairs are often displayed on____ ______ ____ are used to display their relationship

A

Tables of values

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10
Q

3x+4y=9 X-y=0 Or X+2Y=-8

A

The standard form of linear equations in two variables

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12
Q

When you plug in numbers for ordered pairs be sure to use _____ so that you won’t make mistakes

A

Parentheses

DO NOT! 2-2+3-7=12

DO! 2(-2)+3(-7)=12

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13
Q

How to decide if an ordered pair is a solution to an equation____ _____ _____ and then see _____ _____ ____ ____ solution.

A

plug in each number, if the expression is equal to the solution

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13
Q

Tables of values can be displayed either ______ or ____ .

A

Vertically Or Horizontally

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14
Q

A linear equation in two variables that is expressed as y=5 can be also expressed as what?

A

X(0) + Y = 5 This is important to remember when completing tables of values.

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16
Q

To complete a table of value, plug a value into the equation and ___ ____ ____ _____ ____ given.

A

solve for the variable not

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17
Q

The vertical line on the Cartesian coordinate system is called the what?

A

Y axis

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18
Q

Every linear equation has an ____ _____ ______ ____ solutions.

A

infinite pair of ordered pair

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19
Q

The horizontal line on the Cartesian coordinate system is called the what?

A

X axis

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20
Q

The Cartesian coordinate system is named after _____ ____ the French mathematician who is credited for creating it.

A

René Descartes (1596-1650)

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21
Q

The rectangular coordinate system is divided into______ ______that are numbered _______ beginning __________

A

Four quadrants Counterclockwise at 2 o’clock

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22
Q

Together the X axis and the Y axis form a ______ _____ ______

A

Rectangular coordinate system AKA Cartesian coordinate system.

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23
Q

The point at which the X axis and the Y axis meet is called_______, and is labeled ______

A

The origin (0,0)

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24
Q

In terms of plotting ordered pairs, they are refered to as___ _____ of the point.

A

The coordinates

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25
Q

It’s important to note that points ON the axes are ___ _____ _____ quadrant

A

not located on any particular

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26
Q

On a plane both numbers in the ordered pair are needed ____ _____ ____ point

A

to locate a point

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27
Q

Coordinates are also a name for?

A

a point (on the Cartesian coordinate System)

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28
Q

On a plane both numbers from an ordered pair (coordinates) are needed ____ _____ ____ point.

A

to locate a

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29
Q

If points on a diagram can be connected with a straight line then it is said to have a ____ _____

A

Linear relationship.

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30
Q

The two numbers in an ordered pair are called the _____of a corresponding point

A

Coordinates

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30
Q

Every point on a rectangular coordinate system corresponds to_____ _____ _____ equation.

A

the solution of some

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31
Q

The graph of any linear equation in two variables is always a_____ ______

A

Straight-line

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32
Q

A graph of data composed of several ordered pairs used to tell how two quantities relate to each other

A

Scatter diagram.

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33
Q

The process of plotting points and drawing a line through them is called________

A

Graphing

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34
Q

Only two distinct points are needed to determine a straight line, BUT it is always best to what?

A

Graph a third point to be sure

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35
Q

What do you call THE POINT at which a line a particular axis is intercepted by a line ?

A

The intercept Y intercept Or X intercept

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36
Q

What are the coordinates of an intercept (x or y) if it crosses the origin?

A

The intercepts are (0, 0)

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37
Q

How do you find the X intercept?

A

Let Y=0 and solve for X

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38
Q

How do you find the Y intercept?

A

Let X=0 and solve for Y

39
Q

When choosing x or y values to find ordered pairs to plot, do not choose numbers that _____ ______ ______. Make sure that the numbers______

A

numbers that are close together, differ by at least two. DO NOT USE (-1,-1) DO USE (-1,1) Or (0,2)

41
Q

What is the formula to tell whether or not a linear equation in 2 variables passes to the origin of a rectangular coordinate system (cartesian coordinate system).

A

Ax + By = 0

42
Q

A linear equations with one variable, can also be seen as a linear equation with two variables, in which the variable that cannot be seen is actually that variable being _________.

A

multiplied by 0.

43
Q

Horizontal and vertical lines are often confused with each other If Y=K then it’s parallel to the ________ And If X=K then it is parallel to the_______

A

X-axis Y-axis

44
Q

One way to measure the steepness or the slope of the line is to compare___________________ from one point to another.

A

The vertical change in the line with The horizontal change in the line

45
Q

What do you call the change (vertical) in the Y value?

A

Rise

45
Q

What do you call the change (horizontal) in the X value?

A

Run

46
Q

To compare the rise and the run we begin at point Q and _________________ forming_____________.

A

count the amount of spaces from Q to P By creating an imaginary right angle triangle

47
Q

These type of equations always lead to VERTICAL lines respectively.

A

Ax+ 0y=B or 0y=B

48
Q

After you form the right angle counting this distance from point Q to point P what formula do you use to find the SLOPE?

A

Vert. change Y (rise) S = _________ Hori. change X (run)

49
Q

A horizontal line has ____ slope

A

0

50
Q

What is the ordered pair of a completely horizontal line.

A

The ordered pair (0, k) {Horizontal} Intercepts the Y axis but does not intercept the X axis

51
Q

The ratio of the vertical change in Y to the HORIZONTAL change in X.

A

Slope

51
Q

A vertical line has ______slope

A

No Slope (is undefined)

52
Q

These type of equations always lead to horizontal lines respectively.

A

0x+ Ay=B or Ay=B

53
Q

Linear equations in 2 variables problems that only have one variable shown DO NOT intercept the axis for the variable not shown. The intercept is described as…

A

None.

54
Q

What is the ordered pair of a completely vertical line.

A

The ordered pair (k,0) {Vertical} Intercepts the X axis but does not intercept the Y axis

55
Q

What is the Formula for the X axis?

A

Y=0

56
Q

What is the Formula for the Y axis?

A

X=0

59
Q

What is the slope also refered to as/

A

Slant or Steepness

60
Q

What are the two ways to find the slpope of a line?

A

Count the places and divide the rise by the run OR Subtract the run x and y values from the rise x and y values and then the divide the for the y values by difference of the x values.

61
Q

Rise represents the which axis?

A

Y

62
Q

Run represents the which axis?

A

X

63
Q

The slope of any two points on a line are the same as any _____________________________________

A

other two points on the same line, in terms of a ratio.

64
Q

Slope is used in daily situations A stariwell with a slope of 8ft/12 ft means that the stairwell _________

A

rises for every 8 feet for every 12 feet that it runs.

65
Q

If a road has a 10% grade(1 ft/10 ft) that means it________________

A

Rises every 1 ft for every 10 ft that it runs.

66
Q

If a road has a 10% grade(1 ft/10 ft) that means it________________

A

Rises every 1 ft for every 10 ft that it runs.

67
Q

This notation

X1

is called….

A

Subsript notation

68
Q

A way of indicating nonspecific values

such as

x1 and x2

A

Subscript notation.

69
Q

How would you read subscript notation

written like so

x1

x2

A

x sub-one

x sub-two

70
Q

What two nonspecific points can you use to indicate slope?

A

(x1y1)

(x2y2)

71
Q

Traditionally the letter____ represents slope

A

m

72
Q

what is the orginal slope formula?

A

If the nothing in the denominator is ≠ 0

 change in y

m=________

  change in x

or

y2-y1

m=________

x<sub>2</sub>-x<sub>1</sub>
73
Q

The _______ tells you how fast y changes for each unit of change in x

A

slope of a line

74
Q

If the slope is a positive number it moves…

A

Upward from left to right.

75
Q

If th slope is a negative number the line

A

moves downward from left to right.

76
Q

The steeper the slope

A

The greater the absolute value (distance from zero)

77
Q

Th value of a lines intercept is determined by whether or not it crosses ____________________

A

on the positive or negative side of the axis (X or Y).

78
Q

Horizontal lines with equations

of the form

y=k

have

A

slope 0

79
Q

Vertical lines with equations

of the form

x=k

have

A

an undifined slope

80
Q

one linear equation in 2 variables represents…

A

one whole line.

81
Q

In order to find the slope of a line using only one equation

you should _____ and __________________.

Do this until you have _______line.

A

pick a number to plug into the equation

solve for the other variable.

several ordered pair points to form a

82
Q

An easy way to determine the slope of an line by looking at the equation is by reading the equation if the equation solves for y like so

y=ax+b

than the slope of the line is always what???

A

The slope of

y=ax+b

is

a

83
Q

What are two lines on a plane that DO NOT intersect called?

A

Parallel

84
Q

In order to tell if two lines are parallel what do we use?

A

Slopes

85
Q

What do all nonvertical parallel lines always have?

A

Equal slopes

86
Q

What do you do to tell if two equations are parallel?

A

Solve for Y

If the x values are equal they are parallel.

87
Q

If two lines on a plane are parallel with the same slope then they are________

A

Non vertical

88
Q

Two lines that intersect to form a right angle are considered…

A

Perpindicular

89
Q

How do you tell if two angles are perpindicular?

A

If the product of their

slopes = -1

IF

neither of the two is vertical.

90
Q

Slopes of perpindicular lines are _______reciprocals

A

negative (or opposite)

91
Q

What is the negative recirprocal of

3/4

A

-4/3

92
Q

What is the negative recirprocal of

1/2

A

-2/1

or

-2

93
Q

What is the negative recirprocal of

-6

or

-6/1

A

1/6

94
Q

What is the negative recirprocal of

-0.4

or

-4/10

A

10/4

or

2.5

95
Q

The product of each number and it’s negative reciprocal is?

A

-1

Algebra 1 (8 decks)

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