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Learn to represent patterns in linear relations

Grade 9 Math: Master Core Concepts & Problem Solving

Operations with rational numbers

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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

Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

Multiplying decimals

Multiplying Decimals

Dividing decimals

Dividing Decimals

Order of operations (PEMDAS)

Identify the Order of Operations

Order of Operations — Word Problem

Divisibility rules

Divisibility

Determining common factors

Common Factors — Word problem: bouquet

Common Factors — Word problem: party

Common Factors

Factors

Determining common multiples

Common Multiples — Word problem: meals

Common Multiples — Word problem: watches

Multiples

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Introduction to exponents

Expanded powers

Exponents — Express as a power of 10

Exponents — Word problem: express as a power

Exponents — Express as a power of two — Whole number

Place value

Comparing and ordering numbers

Comparing Integers

Comparing Numbers

Comparing Fractions

Rounding numbers

Rounding Decimals

Rounding Integers — Up to 9999

Exponents and exponent laws with whole-number exponents

Using exponents to describe numbers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Operations with polynomials of degree less than or equal to 2

Characteristics of polynomials

What are polynomials

Equivalent expressions of 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

Two-variable linear relations using graphing, interpolation, and extrapolation

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

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Multi-step one-variable 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 linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Solving literal equations

Spatial proportional reasoning

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Statistics in society

Frequency tables and dot plots

Analyze the Frequency Table

Influencing factors in data collection

Data collection

Probability

Advantages and disadvantages of different graphs

Reading and drawing bar graphs

read and draw bar graphs

Reading Bar Graphs

Reading and drawing histograms

Reading and drawing line graphs

Reading Line Graphs

Box-and-whisker plots and scatter plots

Reading and drawing Venn diagrams

Stem and leaf plots

The Leaf and Stem of Numbers

Recognizing the Leaf and Stem of Numbers

Recognizing The Leaf And Stem of Numbers Leaf

Recognizing The Leaf And Stem of Numbers Stem

Reading Stem and Leaf Plots — Median

Reading Stem and Leaf Plots — Range

stem and leaf plots Range

Reading Stem and Leaf Plots

Reading Stem and Leaf Plots — Mean

Reading Stem and Leaf Plots — Mode

Financial literacy - simple budgets and transactions

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

We&apos;ve got you covered with our complete help for Grade 9 math, whether it&apos;s for <a href="http://www.eqao.com/en/assessments/grade-9-math">EQAO</a> (Ontario), grade 9 math <a href="https://education.alberta.ca/provincial-achievement-tests/about-the-pats/">PAT</a> (Alberta), grade 9 math <a href="http://www.ed.gov.nl.ca/edu/k12/evaluation/crts/intermediate/">Provincial Assessment</a> (Newfoundland) or <a href="http://www.gov.pe.ca/eecd/index.php3?number=1027081&lang=E">IMA</a> (PEI).

Aligned with your class or textbook, you will get grade 9 math help on topics like Circle geometry, Linear equations, Dividing polynomials, Exponents, Surface area, Rational numbers, and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 9 math questions. Then, strengthen your understanding with tons of grade 9 math practice. 

All our lessons are taught by experienced Grade 9 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Grade 9

math

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade9math.png

Ex. 1:

Ex. 2:

Ex. 3:

- Let's take a look. We're going to come up with an equation to represent the relationship between the number of sides we have, sorry the number of octagons that we have versus the number of sides that we have right here. This is the input and this is the output. The purpose of this chapter here is to figure out the relationship between the two variables and the relationship is always called the linear. They are all linear functions in this chapter. It's a good thing. Why? 
Because if you're doing linear functions, guess what? You have one equation. It's y equals to mx plus a b. That's the equation you are trying to get. This is the output, which is the y. This is the x, which is the input. Basically, one times something and add another thing should give you that eight over here. It should work for all the points here. Are we going to take a guess or are we going to calculate? Personal suggestion, we should calculate. Because guessing might take forever. What we're going to do is this. It's very simple. We're going to calculate the m and we're calculate the b. To calculate m right now, we're just going to give you an equation. It's very straightforward. It's y2 minus y1 divided by x2 minus the x1. What are the twos? What are the ones? It's just representing the second point versus the first point. And they don't have to be the second versus the first. They can be any two points from your data sets right here. So for example, I can pick the third one versus the second one. But try to pick the later one subtracting the preceding ones. Let's say I pick this set here and let's pick another set right here. What happened here we're just following the equation. It's says y two, so let's say this is my y two, which is right here, the 20 because this is the y and that's the x. This is the second point and this is the first point that we're going to pick. 20 minus 14. Be careful you're subtracting the two y's together. Then x two minus the x one. We've got three minus one. We've got a six over here on the top and a two down here. We've got ourselves a three for our m. You see right here, we've got m right here now which is three. What about b? For b, it's a little bit easier. What happened is, if you write down that equation one more time and this time you can pick any points that you wish. Just pick one. Let's say you pick this one right here. Let's say you like the five better. You put 32 into your y position. The m that you just calculated is a three. The x with the 32, make sure it is coming from the same pair. You're going to put the five right there and there's your b that's missing. Let's do a little bit of math right here for you. We've got 32 equals to 15 plus the b. If you subtract the 15 over to the other side, your b turns out to be 17. That's your b right there. Once you have your b, and once you have your m, guess what happens? Your final answer for this question here is actually just going to be-- therefore, three triangles we're going to go y equals the m, 3x plus the 17 and this is your final answer for this question. Without any guessing, the process may seem a little messy but you just have to remember apply this m calculation right here. Then solve for b by writing down the equation one more time but plug in the m you just calculated which is a three and you can pick any points you like. Just plug it in and you will find the b. Rewrite them one more time, leave out the y, leave out the x. Why is that? Because we're going to put different numbers for x in here to calculate the y for future questions. That's it for this part. Let's take a look at what's happening for the next part.

In this section, we will learn how to represent patterns in linear relations. In other words, these patterns will form a straight line if they are plotted on a graph paper. We can start with creating a table of values which has the independent variable as X, and <a href='[[glossary.html|{"keyword":"Dependent Variable","term":"Dependent Variable"}]]'>dependent variable</a> as Y. One way to represent patterns in linear relations is to use the slope-intercept form.