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Graph linear functions using a slope and point

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. 2

<p>- Hi, welcome to this question right here. So, we're given the point and the slope and we need to draw the graph. Now, this is actually very, very easy. See, what happens is, we don't even need to show any work. Let's say the graph in a standard precision. You do know you have a point, and that point is at negative 3, so you go left 3 and up 2. So you're at somewhere over here, correct? If you have a grid paper, obviously you can do a much better job that I am. So, you know this slope is 2 over 3, so that means you're going from this point, you're gonna go up 2 and over 3 this way. So, let's say just go up 2 right there and you go over 3, so you should be hitting on this point right there. That's 2 points up from here so, if I just kind of draw the little bit of curly direction right here and go over 3. Once you have two points, using the gridded ruler or anything that is straight, and you just simply draw like a straight line connecting the two points and therefore, that's your graph, OK? And that's the final answer. Thanks for watching.</p>

If we are given a single point and the slope of a straight line, we will be able to graph it. By the same token, we can determine the slope and intercepts if we are given from its graph.

Graph using a single point and slope

Graphing linear functions using a single point and gradient

Point-slope form: \(y - y_1 = m (x - x_1)\)