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Table of values for a linear equation

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. 3:

Ex. 2:

- Hi, welcome to this question right here. So we're going to draw a graph using the table of values that's presented to us right beside right here. So remember the X is usually the first one you'll look because X is the input and it's usually found on the x-axis okay? Which that's why it's called the X values, right? 
So I'm going to label these guys the X, and label these guys the Y. Now, I have the X values from four to eight. So looking at the graph right here, if I just call this number here zero, then this number here will be one, and this is two, three, then this obviously will be four, five, six, seven, eight. Let's put a nine right there just to make it look nicer. Now, on the y-axis, I got 21 to 49. Now because there's a little bit more numbers. So what I would suggest is that maybe you just want to keep them-- like going from zero to 50. Okay, zero to 50 will cover everything here, right? Zero to 50 because the highest number is 49, but we&apos;ve got one, two, three, four, five, six, seven, eight, nine, ten. We&apos;ve got 10 boxes. So what we can do is, we can actually cut every two unit is a 10. Okay, because that will give us enough data points. Plus we're going to use all the graph. So there you go, that's all the y-axis over there. So basically each unit or each box is a five. So let's go ahead and actually label it, we say, draw the graph. Show the relationship, so here we go. When X is equals to four which is over here, the Y value is 21. So we just go to where the four is and 21 approximately will be somewhere right there. Okay? And here we have five and 28, we go five and 28 somewhere over here. Six and 35, we&apos;ve got six and all the way to 35. Put a dot right down there. We&apos;ve got also seven and 42. Seven and 42 and the last one, it's the eight and 49. We&apos;ve got eight and 49 right there. So for this part of the question, we're just labeling the dot and it looks like a straight line. Okay, but in order to be certain that it is a straight line, you might need to calculate something, okay? 
For now, the relationship is simple. For every X you have, the Y seems to get bigger and bigger as they go. The greater the X, also the greater the Y. We don't know what they are representing but for sure, it looks like a linear relationship between the two values, okay? Thanks for watching.

Linear equations represent direct proportional relationships between x and y. A table of values contains the exact values of x and y. In this section, we will learn how to draw graphs based on the data from tables of values. From the tables and graphs, we will try to describe and determine whether the relationships are linear or not.

Understanding tables of values of linear relationships

Graphing and writing equations of proportional relationships

Understanding tables of values of proportional relationships