Chapter 3A Flashcards
A type of graph (or a simulation of bars) arranged either vertically or horizontally to show comparisons of data
Bar graph
An organized way of displaying ordered pairs
Tables of values
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
A pair of numbers written in parentheses in which the order of the numbers is important. (-2,7)
Ordered pair
A type of graph used to show changes, or trends in data overtime.
Line graph
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
An ordered pair that is the solution of an equation is said to “______” the equation
Satisfy
When reading an ordered pair the first value is always ___and___ is the second value.
X Y
When reading ordered pairs (2,13) and (13,2) are considered ________
Not the same.
Ordered pairs are often displayed on____ ______ ____ are used to display their relationship
Tables of values
3x+4y=9 X-y=0 Or X+2Y=-8
The standard form of linear equations in two variables
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
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
Tables of values can be displayed either ______ or ____ .
Vertically Or Horizontally
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.
To complete a table of value, plug a value into the equation and ___ ____ ____ _____ ____ given.
solve for the variable not
The vertical line on the Cartesian coordinate system is called the what?
Y axis
Every linear equation has an ____ _____ ______ ____ solutions.
infinite pair of ordered pair
The horizontal line on the Cartesian coordinate system is called the what?
X axis
The Cartesian coordinate system is named after _____ ____ the French mathematician who is credited for creating it.
René Descartes (1596-1650)
The rectangular coordinate system is divided into______ ______that are numbered _______ beginning __________
Four quadrants Counterclockwise at 2 o’clock
Together the X axis and the Y axis form a ______ _____ ______
Rectangular coordinate system AKA Cartesian coordinate system.
The point at which the X axis and the Y axis meet is called_______, and is labeled ______
The origin (0,0)
In terms of plotting ordered pairs, they are refered to as___ _____ of the point.
The coordinates
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
0
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?
Y
Run represents the which axis?
X
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)
(x2y2)
Traditionally the letter____ represents slope
m
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=________
x<sub>2</sub>-x<sub>1</sub>
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
