Chapter 3A Flashcards by Steven Gant

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

Bar graph

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An organized way of displaying ordered pairs

Tables of values

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

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

Ordered pair

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

Line graph

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

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

Satisfy

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

X Y

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

Not the same.

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

Tables of values

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

The standard form of linear equations in two variables

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

Parentheses

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

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

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

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

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Tables of values can be displayed either ______ or ____ .

Vertically Or Horizontally

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

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

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

solve for the variable not

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

Y axis

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Every linear equation has an ____ _____ ______ ____ solutions.

infinite pair of ordered pair

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

X axis

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

René Descartes (1596-1650)

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

Four quadrants Counterclockwise at 2 o’clock

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

Rectangular coordinate system AKA Cartesian coordinate system.

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

The origin (0,0)

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

The coordinates

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It's important to note that points ON the axes are ___ \_\_\_\_\_ _____ quadrant

not located on any particular

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

to locate a point

Coordinates are also a name for?

a point (on the Cartesian coordinate System)

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

to locate a

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

Linear relationship.

The two numbers in an ordered pair are called the \_\_\_\_\_of a corresponding point

Coordinates

Every point on a rectangular coordinate system corresponds to\_\_\_\_\_ _____ \_\_\_\_\_ equation.

the solution of some

The graph of any linear equation in two variables is always a\_\_\_\_\_ \_\_\_\_\_\_

Straight-line

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

Scatter diagram.

The process of plotting points and drawing a line through them is called\_\_\_\_\_\_\_\_

Graphing

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

Graph a third point to be sure

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

The intercept Y intercept Or X intercept

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

The intercepts are (0, 0)

How do you find the X intercept?

Let Y=0 and solve for X

How do you find the Y intercept?

Let X=0 and solve for Y

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

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

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).

Ax + By = 0

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 \_\_\_\_\_\_\_\_\_.

multiplied by 0.

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\_\_\_\_\_\_\_

X-axis Y-axis

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

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

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

Rise

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

Run

To compare the rise and the run we begin at point Q and _________________ forming\_\_\_\_\_\_\_\_\_\_\_\_\_.

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

These type of equations always lead to VERTICAL lines respectively.

Ax+ 0y=B or 0y=B

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

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

A horizontal line has ____ slope

What is the ordered pair of a completely horizontal line.

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

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

Slope

A vertical line has \_\_\_\_\_\_slope

No Slope (is undefined)

These type of equations always lead to horizontal lines respectively.

0x+ Ay=B or Ay=B

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...

None.

What is the ordered pair of a completely vertical line.

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

What is the Formula for the X axis?

Y=0

What is the Formula for the Y axis?

X=0

What is the slope also refered to as/

Slant or Steepness

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

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.

Rise represents the which axis?

Run represents the which axis?

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

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

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

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

If a road has a 10% grade(1 ft/10 ft) that means it\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

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

If a road has a 10% grade(1 ft/10 ft) that means it\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

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

This notation X₁ _{is called....}

Subsript notation

A way of indicating nonspecific values such as x₁ and x₂

Subscript notation.

How would you read subscript notation written like so x₁ x₂

x sub-one x sub-two

What two nonspecific points can you use to indicate slope?

(x₁y₁₎ ## Footnote (x₂y₂₎

Traditionally the letter\_\_\_\_ represents slope

what is the orginal slope formula?

If the nothing in the denominator is ≠ 0 change in y m=\_\_\_\_\_\_\_\_ change in x or y₂-y₁ m=\_\_\_\_\_\_\_\_ x₂-x₁

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

slope of a line

If the slope is a positive number it moves...

Upward from left to right.

If th slope is a negative number the line

moves downward from left to right.

The steeper the slope

The greater the absolute value (distance from zero)

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

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

Horizontal lines with equations of the form y=k have

slope 0

Vertical lines with equations of the form x=k have

an undifined slope

one linear equation in 2 variables represents...

one whole line.

In order to find the slope of a line using only one equation you should _____ and \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_. Do this until you have \_\_\_\_\_\_\_line.

pick a number to plug into the equation solve for the other variable. several ordered pair points to form a

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???

The slope of y=ax+b is a

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

Parallel

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

Slopes

What do all nonvertical parallel lines always have?

Equal slopes

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

Solve for Y If the x values are equal they are parallel.

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

Non vertical

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

Perpindicular

How do you tell if two angles are perpindicular?

If the product of their slopes = -1 IF neither of the two is vertical.

Slopes of perpindicular lines are \_\_\_\_\_\_\_reciprocals

negative (or opposite)

What is the negative recirprocal of 3/4

-4/3

What is the negative recirprocal of 1/2

-2/1 or -2

What is the negative recirprocal of -6 or -6/1

1/6

What is the negative recirprocal of -0.4 or -4/10

10/4 or 2.5

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

-1