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Interpreting and reading linear relation graphs

8.EE.A.1

Using exponents to describe numbers

Expanded powers

auto-gen

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

Parent Assignments

Challenge Zone

Foundation Review

8th Grade Math

sample

math

Intro: Read Linear Relation Graphs

Reading and interpreting linear relation graphs

Ex. 3:

Ex. 2:

Ex. 1:

<p>- Hi and welcome to this question right here. So we&apos;ve got an online clothing company can earn $4 for every t-shirt they sell. We've got a graph right here. It says how many can the company earn by selling 55 t-shirts online, right? We&apos;ve got a graph here trying to tell us the relationship between the profit and the number of t-shirts they sold, right? So graphically, if you want to solve it graphically, you just have to focus on the number they give you, 55 t-shirts. So you go down right here which is where the t-shirts are. You go. . .okay it is kind of hard to figure out 55 is but half way of that is 50 and maybe another half will be 55, approximately. If you're going to do a little line going up and once you hit the graph, you're going to have to go straight across and you get yourself approximately, give or take, halfway between 200 and 250. I would say it's approximately, if I solved graphically, it's about $225, okay?<br />
But now if you want to really figure out the answer to this question, you will need to generate an equation. Now it's a linear equation. It's a straight line. Every time, in math, if you see a straight line, the equation is always called y equals mx plus b, okay? To figure out the equation, you just have to think about his. Where is my m and where is my b? Remember the b is actually known as the y-intercept. But if you just don't even think about that, just don't even think about that. Just think about the question itself. You're earning<br />
$4 for every t-shirt. The money they're going to make, let's call it the profit right here, the profit. Which is the money that you're going to make, it simply equals to every $4 for every t-shirt, right? So let's just call that x. That's it. That is the linear equation right here. See the y is the profit which is the y axis and the m is the 4 which we called it a slope. You'll learn about that in the future. And the x is the number of items that you're selling which is the number of clothes, the t-shirts. The b here is kind of tricky. It actually represents something that we call the y-intercept. Well in this case the y-intercept should be a zero, okay? What happens is that your y is just equal to 4x. So this is the equation. This is the linear equation for this line right here. The amount of profit, the money you are going to make, is equal to $4 times every t-shirt that you make, that you sold. So what we're going to do is we're going to punch in the 55 right here to figure out how much money that we're going to make if I sell 55 t-shirts. So you grab the 55, you times by four. You get yourself $220 and that is very close to our approximation. Let's check out our next problem for this one.</p>


Finding profit from selling 55 t-shirts using a graph and equation

Plotting a scuba diver's depth vs. time on a graph

Finding the time when the diver reaches negative 35 meters

Finding dive distance at 40 minutes using a linear equation

Finding how many T-shirts to sell to earn $200

Plotting a working hours vs. earnings table on a graph

Finding earnings at 3.5 hours by reading the graph

Finding how long it takes to earn $50 using the graph and equation

Linear relations are often expressed in graphs. In this 
section, we will learn how to plot these data of linear relationships into graphs. We will also learn how to read and interpret the graphs to help us answer some word problems. 

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Reading and interpreting linear relation graphs