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Study sets matching "1 algebra linear equations"

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Study sets matching "1 algebra linear equations"

14 terms
Algebra 1: Linear Equations
Rate of change
Slope
The Slope Formula
Positive Slope
Rate of change
Slope
21 terms
Algebra 1 Linear Equations
D
A
D
B
D
A
10 terms
Algebra 1- Linear Equations
Standard Form
Slope Intercept Form
Vertical line
Horizontal line
ax+by=c
y=mx+b
x=a m=undefined
y=b m=0
Standard Form
ax+by=c
Slope Intercept Form
y=mx+b
7 terms
Algebra 1: Systems of Linear Equations
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…
15 terms
Algebra 1 - Linear Equations and Inequalities
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
9 terms
Algebra 1 Linear Equations
Systems of Linear Equations
Solution of a System of Linear Equations
Consistent System of Linear Equations
Inconsistent System of Linear Equations
two or more linear equations involving the same variables.
An ordered pair that satisfies each equation in a system of l…
A system of equations that has at least one solution.
A system of equations that has no solutions. The equations ha…
Systems of Linear Equations
two or more linear equations involving the same variables.
Solution of a System of Linear Equations
An ordered pair that satisfies each equation in a system of l…
28 terms
Algebra 1 - Solving Linear Equations
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.
11 terms
(Algebra 1) - Solving Linear Equations
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
17 terms
Linear Systems of Equations (Algebra 1)
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…
15 terms
1 - Linear Algebraic Equations
Algebraic Notation
Expression
Equation
Inequality
The ability to convert worded sentences and problems into alg…
x^2+3x
x^2+3x=8
x^2+3x>28
Algebraic Notation
The ability to convert worded sentences and problems into alg…
Expression
x^2+3x
20 terms
Algebra 1: Linear Equations (Multi-Step, Matching)
0
2
3
4
0
2
8 terms
Algebra 1-Unit 4 Graphing Linear Equations
slope-intercept form
point-slope form
Standard form
Slope Formula
y= mx + b
Ax + By = C
slope-intercept form
y= mx + b
point-slope form
12 terms
Algebra (2.1) Graphing Linear Equations
coordinate plane
x-axis
y-axis
ordered pair
a graph with x- and y- axes
the horizontal line of a graph
the vertical line of a graph
(x,y) marking a coordinate point on a graph
coordinate plane
a graph with x- and y- axes
x-axis
the horizontal line of a graph
20 terms
Algebra Keystone Review - Module 1 Linear Equations
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
21 terms
Algebra 1 Chapt 6 Linear Equations and Graphs
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
37 terms
Algebra 1 Chapt 6 Linear Equations and Graphs
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
27 terms
Chapter 1: Linear Equations in Linear Algebra
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…
20 terms
Algebra Keystone Review - Module 1 Linear Equations
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
54 terms
Chapter 1: Linear Equations in Linear Algebra
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
12 terms
Algebra 1- Linear Equations Vocabulary
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
12 terms
Solving Linear Equations Algebra 1 Review
-12
-13
-14
-6
10x = -120
4 = x + 17
-21 = x - 7
50 = -5(-4 + x)
-12
10x = -120
-13
4 = x + 17
10 terms
Algebra 1 Test; Linear Equations
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
10 terms
Algebra 1 Chapter 1 Solving Linear Equations
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
10 terms
Algebra 2 - Linear Equations
Linear Function
Linear Equation
Dependent Variable
Independent Variable
Function whose graph is a line.
Represents linear functions.
Y is called this.
X is called this.
Linear Function
Function whose graph is a line.
Linear Equation
Represents linear functions.
6 terms
Algebra 1 Module 7 Linear Equations and Inequalities
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…
8 terms
Algebra I - Systems of Linear Equations
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…
20 terms
Algebra Keystone Review - Module 1 Linear Equations
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
14 terms
EL Algebra Chapter 7: Linear Equations
lattice points
Greek Alphabet
slope
horizontal
places where lines cross on a graph
how steep the line is
sideways, flat
lattice points
places where lines cross on a graph
Greek Alphabet
15 terms
Algebra 1 Module 6 Forms of Linear Equations
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…
12 terms
Linear Algebra: Systems of equations
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…
10 terms
Linear Equations - Algebra
Slope definition
Slope formula
Horizontial
Vertical
rate of change
y2-y1 / x2 - x1
m = 0
m = undefined
Slope definition
rate of change
Slope formula
y2-y1 / x2 - x1
19 terms
linear equations algebra
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 AC = BC. 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…
10 terms
PPHS Algebra 2: Section 2-1 (Solving Linear Equations and Inequalities)
Addition property of equality
Subtraction property of equality
Multiplication property of equality
Division property of equality
Add the same quantity (amount) to both sides, and the equatio…
Subtract the same quantity (amount) from both sides, and the…
Multiply both sides of an equation by the same quantity (amou…
Divide both sides of an equation by the same quantity (amount…
Addition property of equality
Add the same quantity (amount) to both sides, and the equatio…
Subtraction property of equality
Subtract the same quantity (amount) from both sides, and the…
25 terms
Algebra I: Write Linear Equations
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…
42 terms
Algebra 1 Linear Equations in Two Variables
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…
13 terms
Algebra Unit 4: Linear Equations
linear equation
slope
y-intercept
x-intercept
An equation in two variables whose graph is a straight line.
The steepness of a line. A ratio comparing the change in y ov…
The point where a graph crosses the y-axis. The value of the…
The point where a graph crosses the x-axis. The value of the…
linear equation
An equation in two variables whose graph is a straight line.
slope
The steepness of a line. A ratio comparing the change in y ov…
10 terms
Algebra 1: Unit 4 Systems of Linear Equations & Inequalities
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
20 terms
Algebra Vocabulary - Linear Equations
Ordered Pair
y-intercept
Horizontal
Parallel
(x,y)
where the line crosses the y-axis
________________
| |
Ordered Pair
(x,y)
y-intercept
where the line crosses the y-axis
12 terms
Algebra 1 Systems of Linear Equations and Inequalities
system of linear equations
solution of a system
elimination method
substitution method
Two or more linear equations using the same variables.
Any ordered pair (x,y) that makes both equations true in a sy…
A method for solving systems by adding or subtracting equatio…
A method for solving systems by replacing one variable with a…
system of linear equations
Two or more linear equations using the same variables.
solution of a system
Any ordered pair (x,y) that makes both equations true in a sy…
7 terms
Algebra 1 - Unit 2: Linear Equations
Additive Identity
Distributive Property
Literal Equation
Multiplicative Identity
the number 0 (for the real numbers)
a(b + c) = ab + ac or a(b - c) = ab - ac
equation containing more than one variable
the number 1 (for the real numbers)
Additive Identity
the number 0 (for the real numbers)
Distributive Property
a(b + c) = ab + ac or a(b - c) = ab - ac
Algebra 1 Linear Equations in Two Variables
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…
14 terms
Algebra (Chap 2) - Linear Equations
Formula
Solve an Equation
Equivalent Equations
Multi-Step Equations
A mathematical relationship or rule expressed in symbols.
The process of finding all values of the variable that make t…
equations that have the same solution
Equations with more than one operation.
Formula
A mathematical relationship or rule expressed in symbols.
Solve an Equation
The process of finding all values of the variable that make t…
14 terms
Algebra 1 Pre-AP Chapter 4: Equations of Linear Functions
slope intercept form
constant function
constraint
linear extrapolation
the equation of a straight line in the form y = mx + b where…
Consistent horizontal, slope = 0 (Horizontal line)
a condition that a solution must satisfy
The use of a linear equation to predict values that are outsi…
slope intercept form
the equation of a straight line in the form y = mx + b where…
constant function
Consistent horizontal, slope = 0 (Horizontal line)
25 terms
MGSE9-12.A.CED.1 Algebra: Write Linear Equations
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…
14 terms
algebra 1 solving linear equations vocabulary
algebraic expression
numerical expression
like terms
absolute value
an expression that contains at least one variable
An expression that contains only numbers and operations
Expressions that contain the same variables to the same power
The distance a number is from zero on a number line
algebraic expression
an expression that contains at least one variable
numerical expression
An expression that contains only numbers and operations
31 terms
Linear equations forms and terms - Algebra
linear equation
expression
equation
coefficient
An equation in two variables whose graph in a coordinate plan…
A mathematical sentence without an equal sign.
A mathematical sentence that contains an equal sign.
A number multiplied by a variable in an algebraic expression…
linear equation
An equation in two variables whose graph in a coordinate plan…
expression
A mathematical sentence without an equal sign.
10 terms
3 Algebraic Linear Equations
inconsistent equation
consistent equation
identity
equivalent equations
an equation with no solution
an equation with one solution
an equation that is true for all values of the variable
equations that have the same solution... EX: x+1=9 and x-2=6 bot…
inconsistent equation
an equation with no solution
consistent equation
an equation with one solution
Linear Algebra Section 1.3: Vector equations
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?
linear equations algebraic
the coefficents of one variable must b…
cross out the negative and positive va…
add the two equations to eliminate the…
plug your answer from step 3 into eith…
step 1
step 2
step 3
step 4
the coefficents of one variable must b…
step 1
cross out the negative and positive va…
step 2
Linear Algebra Section 1.4: Matrix Equations
Matrix equation
Vector equation
Ax = b has a solution =>
Using the definition of "Ax", how do y…
Ax = b
x1v1 + x2v2 + ... + XnVn = b
b is in the spam of colums of "A"
...
Matrix equation
Ax = b
Vector equation
x1v1 + x2v2 + ... + XnVn = b
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