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Master Solving Systems of Linear Equations by Graphing

8.EE.A.1

Using exponents to describe numbers

Expanded powers

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Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

8.EE.A.2

Squares and square roots

Square Root of a Perfect Square

Square and square roots

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

Converting radicals to entire radicals

8.EE.A.3

Scientific notation

8.EE.B.5

Parallel and perpendicular lines in linear functions

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Identifying proportional relationships

8.EE.B.6

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

8.EE.C.7

Introduction to linear equations

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Two-step Linear Equations LHS

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Two-step Linear Equations RHS

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Solving literal equations

8.EE.C.8

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

8.F.A.1

Relationship between two variables

Identifying functions

8.F.A.2

Function notation

8.F.B.4

Applications of linear relations

8.F.B.5

Graphing linear functions using table of values

8.G.A.1

Line symmetry

Tessellations using translations and reflections

tessellations using translations and reflections

8.G.A.2

Rotational symmetry and transformations

8.G.A.3

Enlargements and reductions with scale factors

Tessellations using rotations

8.G.A.4

Similar polygons

8.G.A.5

Similar triangles

8.G.B.6

Pythagorean theorem

Pythagorean Theorem

8.G.B.7

Using the pythagorean relationship

8.G.B.8

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Applications of pythagorean theorem

8.G.C.9

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area and volume of cones

Surface area and volume of spheres

8.NS.A.1

Understanding the number systems

Rational vs. Irrational numbers

8.NS.A.2

Determine square roots of rational numbers

Square roots of rational numbers

Estimating square roots

Converting repeating decimals to fractions

8.SP.A.1

Reading linear relation graphs

Box-and-whisker plots and scatter plots

8.SP.A.2

Solving linear equations by graphing

8th Grade Math

sample

math

Intro

Ex. 1

Intro to solving systems of linear equations by graphing

Three methods for graphing systems of linear equations

- Hello, welcome to this question right here. We're trying to graph these two equations here, and figure out a way they intersect each other, or not, right? 
So, let's go ahead and actually solve in terms of y equals mx plus b, because that's the easiest way to graph this. So, I'm gonna move the y over here and move the negative nine on this side to solve the y. So, I've got myself a 2x plus nine. And this one over here is just going to be, let me do a little bit work here, I'm gonna move the negative x over and I get this, divide everything by three, okay? 
So, now my second equation says negative one over three x plus two, okay? Now, if you have a grid paper, or just a piece of paper is fine, because we're just gonna do a rough sketch to figure out where they intersect each other. So, I've got a positive nine on top, one, two, three, four, five, six, seven, eight, nine. There's a point right there for the first equation, and it's going in this direction, up to over one. That's the slope right there. So, in another way, you can actually do the other direction. So, instead of going up two over one because I ran out of space, I can go down two left one, which is here. And down two left one, which is here. So, I've got myself a nice single straight graph coming down this way, okay? 
Now, if you do the second equation quickly it's actually, your y intercepts at the point y equals two, and the slope is this direction, because it's negative. So, you go down one and over three. So, you go down one and over three, so one, two, three, you're somewhere over here. Two points usually gives you a good point so we're gonna draw a line over here, draw a line over here. Sorry it's not right going straight.okay? 
We've got a little approximate point right here, which is right over here, okay? 
That's a point of intersection. Now, if you're wondering what that point is, it happens at negative three, and a positive three, okay? So, if you have a grid paper, grid paper you can actually plot them really good. And you will see that the both lines right here intersect each other at negative three, and three. Thanks for watching.

Solving a system of linear equations using slope-intercept graphing

Identifying parallel lines with no solution using the intercept method

Graphing two linear equations to find their intersection point

Discovering two equations that simplify to the same line

In order to determine the number of solutions to a system of linear equations, other than by finding the slope of the lines, we can also graph the equations out and look for the intersection of the lines.