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Interpreting and reading linear relation graphs

EQAO Grade 9 Math: Master Core Concepts & Skills

Ratios, Rates, and Proportions

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Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Pythagorean Theorem

Introduction to pythagorean theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

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

Proportional Relationships

Understanding graphs of proportional relationships

Linear relations

Using tables of values to graph proportional relationships

Linear relation

Applications of proportional relationships

Identifying proportional relationships

Linear Ralations

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

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

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

Midpoint formula: $M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)$

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

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

General form: Ax + By + C = 0

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

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

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplication and Division of 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

Introduction to 3-Dimensional Objects

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

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Data Management

Influencing factors in data collection

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Linear Programming

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

EQAO Grade 9 Principles of 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.

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. 

Understanding graphs of linear relationships

Understanding tables of values of linear relationships

Applications of linear relationships