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Solving Linear Equations by Graphing: Time-Distance Relationships

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

Intro

Ex. 1:

Ex. 2:

Ex. 3:

Ex. 4:

- Hi, welcome to this question right here. So we&apos;ve got a graph here set up for us already, trying to show us the relationship between the temperature in degree Celsius versus the time underneath right here which is in minute, okay? It looks like a very straight single straight lines. So guess what, if you see a straight line it means you're looking at a y equals mx plus b graph, okay? 
Now remember, the y is your y-axis. So in this case I'm going to put down the degree Celsius right here in the position of the y. The m, if you don't remember what m is, it's the slope of the graph, okay? So we're going to figure out the slope later. The x, so we draw a box with a slope and the x is the x axis. So it's in the time and we just use the variable t, but just remember as in terms of a minute for this question. Now the b is known as the y-intercept on the graph. The y-intercept is where the graph would touch the y-axis. If I just kind of look at the graph right here. If it is just going straight down like this, it will probably enter the zero go across the zero. So in this question here, you don't have a b for your equation, okay? Just leave it out, but the problem is how do you figure out the slope? Well remember, you might want to learn it right now, the slope is equal to the rise over run, okay? It's basically how the graphs behaves, going up first and turn left or right. Now, this is how we do it. You can pick two points. Let's say I pick these two points right here. Now just ask yourself, 
"How can I go from here to here?" Well, if I'm just using the rise over run which is the slope, which is the m over here, okay? 
All we had to do is just think about that in order for me to go from here to here, I need to go up 20 units first, okay? So this is 20, this is 40, so the difference is that I need to go up 20. So the rise in this case will be 20 and it's positive. Why, because you're going up. If you're going down, it'll be negative. Okay? Then in order for me to go from this point to here, I need to travel from two minutes to four minutes. That's a difference of two minutes. So that means I need to go to my right side two minutes. So it's positive because you're going toward the right. If you're going towards the left, it's negative. Okay? So 20 over two, what do you get? You don't need a calculator for that, at least for me I don't need one. Ten, okay so the 10 is actually your slope which is represented by the m in the equation. So guess what, it goes in here, 10t okay? 
So the relationship between the degree Celsius right here versus the time is just that the degree, the temperature is equal to 10 times the t, that's it. So the equation here, the equation for that relationship is right over here. You can either use this one right here or feel free to go y equals to 10 times the x. You can also use this equation, okay? Oh, where did it go? 
Y equals to 10 times the x, okay? So that way, it's easier. All right, but if you want to use the variables from the question, then it will be the degree Celsius equals the 10 times the t. All right? Let's check on the next--

We will learn how to plot linear equations, and then use the graphs as an aid to answer questions about the linear relations. Alternatively, we can find out the linear equations from their graphs. In addition, we will learn how to plot graphs and determine their equations when we are given the table of values of linear relations. We will also explore the concepts of interpolating and extrapolating data from graphs of linear equations.  

Solving linear systems by graphing

Solving systems of linear equations with graphing