#### Study sets matching "1 algebra linear equations"

#### Study sets matching "1 algebra linear equations"

coordinate plane

origin

x-axis

y-axis

the grid created by the horizontal x-axis and the vertical y-…

(0,0) in the coordinate plane; center of the grid

the horizontal number line in the coordinate plane (left to r…

the vertical number line in the coordinate plane (up and down)

coordinate plane

the grid created by the horizontal x-axis and the vertical y-…

origin

(0,0) in the coordinate plane; center of the grid

elimination method

linear inequality

solution of a system of linear inequal…

solution of a system of linear equations

solving systems by adding or subtracting equations to elimina…

an inequality in two variables whose graph is a region of the…

a set of values that make all inequalities in a system true.…

a set of values that make all equations in a system true. [p.…

elimination method

solving systems by adding or subtracting equations to elimina…

linear inequality

an inequality in two variables whose graph is a region of the…

coefficient

distributive property

equation

inequality

the numerical part of a term

for any numbers a, b, and c: a(b+c) = ab+bc

a mathematical sentence showing two expressions are equal

mathematical sentences having the symbols <,>

coefficient

the numerical part of a term

distributive property

for any numbers a, b, and c: a(b+c) = ab+bc

rise

run

slope

dependent

vertical change... the difference in the y-values on a line

horizontal change... the difference in the x-values on a line

Slope= Rise/Run=Change in Y/Change in X... m = y₂-y₁/ x₂-x₁

Variable that changes as a result of a change in the independ…

rise

vertical change... the difference in the y-values on a line

run

horizontal change... the difference in the x-values on a line

consistent system

dependent system

elimination method

inconsistent system

a system of equations or inequalities that has at least one s…

a system of equations that has infinitely many solutions

a method used to solve systems of equations in which one vari…

a system of equations or inequalities that has no solution

consistent system

a system of equations or inequalities that has at least one s…

dependent system

a system of equations that has infinitely many solutions

Function

Function Notation

Input

Output

A relationship where each input has exactly one output.

If x is input and y is the output, then the function notation…

A number in the domain of a function. ... The independent variab…

A number in the range of a function.... The dependent variable.

Function

A relationship where each input has exactly one output.

Function Notation

If x is input and y is the output, then the function notation…

conjecture

theorem

rule

linear equation in one variable

An unproven statement about a general mathematical concept, e…

A proven statement about a general mathematical concept.

A term used in place of the word theorem.

An equation that can be written as ax + b = 0, where a ≠ 0.

conjecture

An unproven statement about a general mathematical concept, e…

theorem

A proven statement about a general mathematical concept.

The slope of the line passing through…

The slope of the line passing through…

The slope of the line passing through…

Slope

m = 0

Slope is Undefined

m = 1

The steepness of a line

The slope of the line passing through…

m = 0

The slope of the line passing through…

Slope is Undefined

What is a linear equation?

What is a system of linear equations?

What is a solution of a linear equation?

What is a solution set?

Any equation that can be written in the following form: (pg. 2)

A system of linear equations (or a linear system) is a collec…

A list of numbers that satisfies a system of linear equations…

The set of all possible solutions is called the solution set…

What is a linear equation?

Any equation that can be written in the following form: (pg. 2)

What is a system of linear equations?

A system of linear equations (or a linear system) is a collec…

The slope of the line passing through…

The slope of the line passing through…

Slope

Y-Intercept

m = 0

Slope is Undefined

The steepness of a line

Where a line crosses the y-axis

The slope of the line passing through…

m = 0

The slope of the line passing through…

Slope is Undefined

System of linear equations

Solve graphically

Solution to a system of linear equations

Infinite solutions

2 or more linear equations

Use a graph to find the solution

The point at which 2 linear equations intersect.

The number of solutions a system has when the graphs of the e…

System of linear equations

2 or more linear equations

Solve graphically

Use a graph to find the solution

linear equation in one variable

solution of an equation

inverse operation for addition

inverse operation for subtraction

An equation that can be written as ax + b = 0, where a ≠ 0.

a value that makes the equation true

subraction

addition

linear equation in one variable

An equation that can be written as ax + b = 0, where a ≠ 0.

solution of an equation

a value that makes the equation true

Equation

Equivalent Equations

Identity

Inverse operations

a statement formed when an equal sign is placed between two e…

Equations that have the same solution as the original equation

An eqaution that is true for all values of the variables

operations that undo each other

Equation

a statement formed when an equal sign is placed between two e…

Equivalent Equations

Equations that have the same solution as the original equation

Solve

Point of Intersection

Absolute Value Equations

Absolute Value Inequalities

Find the value of a variable

The point where two or more lines or curves cross

An equation containing absolute value symbols

An inequality containing absolute value symbols

Solve

Find the value of a variable

Point of Intersection

The point where two or more lines or curves cross

conjecture

theorem or rule

equation

linear equation in one variable

an unproven statement about a general mathematical concept

a proven statement about a general mathematical concept

a statement that two expressions are equal

an equation that can be written in the form ax + b = 0, where…

conjecture

an unproven statement about a general mathematical concept

theorem or rule

a proven statement about a general mathematical concept

Linear Equation

Linear System

Solution

Solution Set

An equation that can be written in the form:... a1x1+a2x2+...+an…

A collection of one or more linear equations involving the sa…

A list (s1, s2, ..., sn) of numbers that makes each equation…

The set of all possible solutions for a given system

Linear Equation

An equation that can be written in the form:... a1x1+a2x2+...+an…

Linear System

A collection of one or more linear equations involving the sa…

x<-9

8

(1, 1)

x<2 or x >20

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

Solve for x:... 4(x-5)=12

What is the solution?... (hint: 2nd, CALC, 5, enter, enter, ente…

Solve this compound "or" inequality:... 5x<10 or .5x>10

x<-9

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

8

Solve for x:... 4(x-5)=12

When is a system of linear equations c…

When is a system of linear equations i…

When do 2 linear systems have the same…

(Row) Echelon Form

When it has either one solution or infinitely many solutions

When it has no solution

If their augmented matrices are row equivalent

1) All nonzero rows are above any rows of all zeros... 2) Each l…

When is a system of linear equations c…

When it has either one solution or infinitely many solutions

When is a system of linear equations i…

When it has no solution

consistent

dependent

elimination

inconsistent

a system of linear equations that has at least one ordered pa…

a system of linear equations that has an infinite number of s…

the use of addition or subtraction to eliminate one variable…

a system of equations with no ordered pair that satisfies bot…

consistent

a system of linear equations that has at least one ordered pa…

dependent

a system of linear equations that has an infinite number of s…

Linear Equation

Standard Form

Rules of Standard Form

To graph on a calculator

An equation that forms a straight line when graphed. It does…

Ax + By = C

- A has to be greater than or equal to zero... - A and B are bot…

Y=, enter the number, GRAPH

Linear Equation

An equation that forms a straight line when graphed. It does…

Standard Form

Ax + By = C

elimination method

linear inequality

solution of a system of linear inequal…

solution of a system of linear equations

solving systems by adding or subtracting equations to elimina…

an inequality in two variables whose graph is a region of the…

a set of values that make all inequalities in a system true.

a set of values that make all equations in a system true.

elimination method

solving systems by adding or subtracting equations to elimina…

linear inequality

an inequality in two variables whose graph is a region of the…

Inverse Operations

Equivalent Equations

Identity

Ratio

Two operations that undo each other.

Equations that have the same solutions.

An equation that is true for all values of the variable.

A comparison of two numbers using division.

Inverse Operations

Two operations that undo each other.

Equivalent Equations

Equations that have the same solutions.

x<-9

8

(1, 1)

x<2 or x >20

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

Solve for x:... 4(x-5)=12

What is the solution?... (hint: 2nd, CALC, 5, enter, enter, ente…

Solve this compound "or" inequality:... 5x<10 or .5x>10

x<-9

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

8

Solve for x:... 4(x-5)=12

slope intercept form

point slope form

y - intercept

How to Write a Linear Function... Ex: Wri…

where m is the slope and (x1, y1) is a point on the line... Thi…

the y-coordinate of the point where the line crosses the y-axis

1 - Write ƒ(0) = 5 as (0, 5) and ƒ(4) = 17 as (4, 17)... 2 - Cal…

slope intercept form

point slope form

where m is the slope and (x1, y1) is a point on the line... Thi…

Point-Slope Form

Converse of a conditional

Perpendicular Lines

Scatter Plot

An equation of a non-vertical line written in form y-y1 = m(x…

A statement formed by interchanging the hypothesis and the co…

Two lines in the same plane that intersect to form a right an…

A graph used to determine whether there is a relationship or…

Point-Slope Form

An equation of a non-vertical line written in form y-y1 = m(x…

Converse of a conditional

A statement formed by interchanging the hypothesis and the co…

parallel lines

perpendicular lines

linear inequality in two variables

solution of an inequality in two varia…

Two different non-vertical lines that have the same slope

Two non-vertical lines in the same plane whose slopes have a…

Can be written in one of the following forms: Ax + By < C, Ax…

One or more ordered pairs that make the inequality true.

parallel lines

Two different non-vertical lines that have the same slope

perpendicular lines

Two non-vertical lines in the same plane whose slopes have a…

Subtraction Property of Equality

Addition Property of Equality

Division Property of Equality

Multiplication Property of Equality

If a = b, then a - c = b - c. Subtracting equal amounts from…

If a = b, then a + c = b + c. Adding equal amounts to each si…

If a = b and c does not equal 0, then a/c = b/c. Dividing eac…

If A = B, then A

**C = B**C. Multiplying each side of an equatio…Subtraction Property of Equality

If a = b, then a - c = b - c. Subtracting equal amounts from…

Addition Property of Equality

If a = b, then a + c = b + c. Adding equal amounts to each si…

Suppose we have a final solution set o…

How are two linear systems equivalent?

How do you solve a linear system?

A matrix with size 3x4 is: ___________…

infinite

They share the same solution sets

Replace the l.s. with one that is equivalent but "simpler", t…

augumented matrix

Suppose we have a final solution set o…

infinite

How are two linear systems equivalent?

They share the same solution sets

The Rectangular Coordinate System

On the x-axis

On the y-axis

We can represent a specific location,…

is made up of a horizontal number line and a vertical number…

the positive direction is to the right and the negative direc…

the positive direction is up and the negative direction is do…

These two numbers make up an ordered pair; we write an ordere…

The Rectangular Coordinate System

is made up of a horizontal number line and a vertical number…

On the x-axis

the positive direction is to the right and the negative direc…

Slope-Intercept Form of an Equation

Point-Slope Form

Family of Functions

Parent Function

If a line has slope m and y-intercept (0, b), then the line i…

The line with slope m that contains the point (x₁, y₁) can be…

A set of functions whose graphs have basic characteristics in…

The most basic function of a family of functions.

Slope-Intercept Form of an Equation

If a line has slope m and y-intercept (0, b), then the line i…

Point-Slope Form

The line with slope m that contains the point (x₁, y₁) can be…

The Rectangular Coordinate System

On the x-axis

On the y-axis

We can represent a specific location,…

is made up of a horizontal number line and a vertical number…

the positive direction is to the right and the negative direc…

the positive direction is up and the negative direction is do…

These two numbers make up an ordered pair; we write an ordere…

The Rectangular Coordinate System

is made up of a horizontal number line and a vertical number…

On the x-axis

the positive direction is to the right and the negative direc…

x<-9

8

(1, 1)

x<2 or x >20

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

Solve for x:... 4(x-5)=12

What is the solution?... (hint: 2nd, CALC, 5, enter, enter, ente…

Solve this compound "or" inequality:... 5x<10 or .5x>10

x<-9

Solve this inequality:... (hint: flip the symbol when you ÷ or ×…

8

Solve for x:... 4(x-5)=12

Indepent System

Inconsistent Sytem

Dependent System

Consistent

The lines intercept at 1 point and have 1 unique solution

The lines are parallel have no solution.

There are two equations for the same line. They have an infin…

(Intercepts)

Indepent System

The lines intercept at 1 point and have 1 unique solution

Inconsistent Sytem

The lines are parallel have no solution.

How can a linear system and their prop…

R^n

Vectors in R^2 represents:

Geometric interpretation

Using th concept of vectors

the set of all vectors of size n?

v = (v1, v2)

u + v represented by a diagonal arrow in a parallelogram

How can a linear system and their prop…

Using th concept of vectors

R^n

the set of all vectors of size n?

Graphically, a system of equations has…

Graphically, a system of equations has…

The three possible solutions for a sys…

A system has infinite solutions if:

They are parallel lines. They never intersect so there's no w…

at the point of intersection. The point where lines have a co…

- no solution... - infinite solutions ... - a unique solution

The equations are equal.... Same slope and y-intercept.

Graphically, a system of equations has…

They are parallel lines. They never intersect so there's no w…

Graphically, a system of equations has…

at the point of intersection. The point where lines have a co…

System of Equations

System of Inequalities

Consistent

Inconsistent

A set of equations with the same variables.

A set of two or more inequalities with the same variables

A system of equations that has at least one solution is consi…

A system of equations that has no solution.

System of Equations

A set of equations with the same variables.

System of Inequalities

A set of two or more inequalities with the same variables