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How to read graphs of linear relationships

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. 1:

Ex. 2:

- Hi, welcome to this question right here. So we've got a little graph right here trying to show you some kind of relationship. So what we have here is the cost of the chocolate bars, okay? So we've got the y-axis and the x-axis here. So remember the x-axis is your independent variables. Here we have the number of the chocolate bars, okay? So we've got one all the way up to 10. Over here, on the y-axis, you've got the cost of the chocolate bars. So if you see, here it is, there's a one, two, three, four, five, six, seven dots. These dots are telling you the number of chocolates and their price according to the number of chocolates you're buying. So let's say, for example, if you have one chocolate bar right here, let me fill the table right here for you. You've got one chocolate bar it's gonna cost you $2, okay? Now, if you're buying two it's gonna cost you $4, okay? And if you buy three it's gonna cost you $6, okay? So. . . 
and so on until you get the 6 chocolate bars, it's gonna cost you $12. So what's the relationship or the pattern that's represented by this graph right here? 
Well, the pattern is that for every chocolate bar that you bought, it's a $2 increase, okay, and you probably got that already just by looking at the first one. Every chocolate bar is $2, okay? So every time you increase your chocolate bar by one, of course, over here you'll increase by two, okay? So that's the pattern. Basically, every chocolate bar is gonna cost you $2, okay? Thanks for watching.

Without understanding and analyzing, graphs of linear relationships are just lines and dots. In this lesson, we will learn the skills to analyze the graphs and get useful information from them.

Understanding graphs of linear relationships

Understanding graphs of proportional relationships 