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Learn to represent patterns in linear relations

Grade 9 Math: Master Core Concepts & Problem Solving

Symmetry and Surface Area

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Rational Numbers

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Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

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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

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

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

Multiplication and Division of Polynomials

Multiplying and dividing polynomials 

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

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

Solving literal equations

Linear Inequalities

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Express linear inequalities graphically and algebraically

Graph the Inequality

Linear Inequalities – Word Problem 

Linear inequalities

Solving one-step linear inequalities

One-step Linear Inequalities

One-step linear inequalities

One-step Linear Inequalities Decimal

One-step Linear Inequalities Decimal with Fraction

One-step Linear Inequalities Fraction

Solve One Step Linear Inequalities Find Solution– Word Problem

One-step Linear Inequalities — Word Problem

Solving multi-step linear inequalities

Multi-step Linear Inequalities

Two-step Linear Inequalities

Multi-step linear inequalities

Two-step linear inequalities

Solve Multi-step Linear Inequalities – Word Problem 

Solve Multi Step Linear Inequalities Solve Equation – Word Problem

Solve Multi Step Linear Inequalities Equation – Word Problem

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Data Collection

Influencing factors in data collection

Data collection

Probability

Parent Assignments

Challenge Zone

Foundation Review

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

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math

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Ex. 1:

Ex. 2:

Ex. 3:

Building a table from square tile figures

Using slope formula to find the linear equation from a table

Finding the figure number that gives 84 squares

Finding the number of squares in figure 14 using the linear equation

Verifying the equation y = 4x + 1 against each figure

Building a table for connected octagons and their side counts

- 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.

Deriving the linear equation from the octagon pattern table

Finding the number of sides for 15 octagons using the equation

Finding the number of octagons given 84 sides

Writing a linear equation from a table of values

Writing a linear equation from a table with decimal values

Finding a linear equation from a table with decimal values

Writing a linear equation from a table using slope and y-intercept

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.

Understanding graphs of linear relationships

Understanding tables of values of linear relationships

Applications of linear relationships

Representing patterns in linear relations

What You'll Learn

Recognize and analyze patterns that form linear relationships

Create tables of values with independent (x) and dependent (y) variables

Calculate the slope (m) using the formula (y2-y1)/(x2-x1)

Determine the y-intercept (b) by substituting known values

Write linear equations in slope-intercept form (y = mx + b)

What You'll Practice

Counting elements in visual patterns and organizing data in tables

Calculating slope from coordinate pairs with whole numbers and decimals

Solving for the y-intercept using the linear equation

Writing complete linear equations from tables of values

Using linear equations to predict values for given inputs

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

13 Video lessons

Practice exercises

Skills

Linear Relations

Slope

Y-Intercept

Tables of Values

Slope-Intercept Form

Patterns

Coordinate Pairs