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Interpreting and reading linear relation graphs

PAT: Master Provincial Achievement Test Skills

Operations with Decimals

test

Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

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Multiplying decimals

Multiplying Decimals

Dividing decimals 

Dividing Decimals

Order of operations (BEDMAS)

Mixed Operations with Decimals

Mixed Operations

Identify the Order of Operations

Order of Operations — Word Problem

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Introduction to Linear Relations

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Linear Relations

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

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

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

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

Solving linear equations with variables on both sides

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

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

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

Solve Linear Equations Using Distributive Property – Word Problem

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

What is a polynomial?

Classifying Polynomials

Polynomial components

Operations with 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

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Surface Area of 3D Objects

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Symmtery

Line symmetry

Rotational symmetry and transformations

Influencing factors in data collection

Data collection

Probability

Provincial Achievement Test

sample

math

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Ex. 3:

Ex. 2:

Ex. 1:

- 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? 
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 
$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.

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. 

Reading linear relation graphs

What You'll Learn

Read and interpret linear graphs to extract data points and values

Use graphical methods to estimate solutions by tracing coordinates on a line

Generate linear equations from graphs and real-world scenarios

Calculate exact solutions using the equation y = mx + b for linear relations

Plot ordered pairs from tables to create accurate linear graphs

What You'll Practice

Estimating values from graphs by reading x and y coordinates

Solving word problems about profit, distance, and wages using graphs

Creating linear equations and substituting values to find unknowns

Plotting data points from tables and drawing best-fit lines

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

8 Video lessons

Skills

Linear Equations

Graphing

Coordinate Plane

Slope

Y-intercept

Data Interpretation

Word Problems