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Table of values for a linear equation

TX.AR.2.A

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Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Rate of change

Applications of linear relations

Arithmetic sequences

Geometric sequences

TX.AR.2.B

Relationship between two variables

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Characteristics of quadratic functions

TX.AR.2.C

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Graphing quadratic functions: General form VS. Vertex form

TX.AR.2.D

Word problems of graphing linear functions

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Applications of quadratic functions

TX.AR.3.A

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

Quadratic function in general form: y = ax^2 + bx + c

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Graphing exponential functions

TX.AR.3.B

Combining transformations of functions

Inverse functions

Even and odd functions

TX.AR.3.C

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

TX.AR.3.D

Operations with functions

TX.AR.3.E

One to one functions

Function notation (advanced)

Composite functions

TX.AR.3.F

Difference quotient: applications of functions

TX.AR.4.A

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplying and dividing monomials

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Multiplying polynomial by polynomial

TX.AR.4.B

Inequalities of combined functions

Inequalities of Combined Functions

TX.AR.4.C

Polynomial long division

Polynomial synthetic division

TX.AR.4.D

Solving polynomials with the unknown 

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Rational zero theorem

Rational Zero Theorem

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

TX.AR.5.A

Adding and subtracting matrices

TX.AR.5.B

Matrix multiplication

TX.AR.5.C

Scalar multiplication of matrices

TX.AR.5.D

System of linear equations

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

TX.AR.5.E

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

The Inverse of a 2 x 2 matrix

The inverse of 3 x 3 matrices with matrix row operations

The inverse of 3 x 3 matrix with determinants and adjugate

2 x 2 invertible matrix

Solving linear systems using Cramer's Rule

Solving linear systems using Cramer"s Rule

Cramer"s Rule with 2 x 2 matrices

Solving linear systems using 2 x 2 inverse matrices

TX.AR.6.B

Introduction to linear equations

Solving quadratic equations by factoring

TX.AR.6.C

Solving logarithmic equations

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Solving exponential equations using exponent rules

TX.AR.7.A

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

TX.AR.7.C

Regression analysis

TX.AR.7.D

Equation of the best fit line

Algebraic Reasoning 

Modeling from data

Number and algebraic methods

Patterns and structure

math

Ex. 1:

Ex. 3:

Ex. 2:

<p>- Hi, welcome to this question right here. So we're going to draw a graph using the table of values that's presented to us right beside right here. So remember the X is usually the first one you'll look because X is the input and it's usually found on the x-axis okay? Which that's why it's called the X values, right?<br />
So I'm going to label these guys the X, and label these guys the Y. Now, I have the X values from four to eight. So looking at the graph right here, if I just call this number here zero, then this number here will be one, and this is two, three, then this obviously will be four, five, six, seven, eight. Let's put a nine right there just to make it look nicer. Now, on the y-axis, I got 21 to 49. Now because there's a little bit more numbers. So what I would suggest is that maybe you just want to keep them-- like going from zero to 50. Okay, zero to 50 will cover everything here, right? Zero to 50 because the highest number is 49, but we&apos;ve got one, two, three, four, five, six, seven, eight, nine, ten. We&apos;ve got 10 boxes. So what we can do is, we can actually cut every two unit is a 10. Okay, because that will give us enough data points. Plus we're going to use all the graph. So there you go, that's all the y-axis over there. So basically each unit or each box is a five. So let's go ahead and actually label it, we say, draw the graph. Show the relationship, so here we go. When X is equals to four which is over here, the Y value is 21. So we just go to where the four is and 21 approximately will be somewhere right there. Okay? And here we have five and 28, we go five and 28 somewhere over here. Six and 35, we&apos;ve got six and all the way to 35. Put a dot right down there. We&apos;ve got also seven and 42. Seven and 42 and the last one, it's the eight and 49. We&apos;ve got eight and 49 right there. So for this part of the question, we're just labeling the dot and it looks like a straight line. Okay, but in order to be certain that it is a straight line, you might need to calculate something, okay?<br />
For now, the relationship is simple. For every X you have, the Y seems to get bigger and bigger as they go. The greater the X, also the greater the Y. We don't know what they are representing but for sure, it looks like a linear relationship between the two values, okay? Thanks for watching.</p>


Linear equations represent direct proportional relationships between x and y. A table of values contains the exact values of x and y. In this section, we will learn how to draw graphs based on the data from tables of values. From the tables and graphs, we will try to describe and determine whether the relationships are linear or not.