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Solving Linear Equations by Graphing: Time-Distance 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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Intro

Ex. 1:

Ex. 2:

Ex. 3:

Ex. 4:

- Hi, welcome to this question right here. So we&apos;ve got a graph here set up for us already, trying to show us the relationship between the temperature in degree Celsius versus the time underneath right here which is in minute, okay? It looks like a very straight single straight lines. So guess what, if you see a straight line it means you're looking at a y equals mx plus b graph, okay? 
Now remember, the y is your y-axis. So in this case I'm going to put down the degree Celsius right here in the position of the y. The m, if you don't remember what m is, it's the slope of the graph, okay? So we're going to figure out the slope later. The x, so we draw a box with a slope and the x is the x axis. So it's in the time and we just use the variable t, but just remember as in terms of a minute for this question. Now the b is known as the y-intercept on the graph. The y-intercept is where the graph would touch the y-axis. If I just kind of look at the graph right here. If it is just going straight down like this, it will probably enter the zero go across the zero. So in this question here, you don't have a b for your equation, okay? Just leave it out, but the problem is how do you figure out the slope? Well remember, you might want to learn it right now, the slope is equal to the rise over run, okay? It's basically how the graphs behaves, going up first and turn left or right. Now, this is how we do it. You can pick two points. Let's say I pick these two points right here. Now just ask yourself, 
"How can I go from here to here?" Well, if I'm just using the rise over run which is the slope, which is the m over here, okay? 
All we had to do is just think about that in order for me to go from here to here, I need to go up 20 units first, okay? So this is 20, this is 40, so the difference is that I need to go up 20. So the rise in this case will be 20 and it's positive. Why, because you're going up. If you're going down, it'll be negative. Okay? Then in order for me to go from this point to here, I need to travel from two minutes to four minutes. That's a difference of two minutes. So that means I need to go to my right side two minutes. So it's positive because you're going toward the right. If you're going towards the left, it's negative. Okay? So 20 over two, what do you get? You don't need a calculator for that, at least for me I don't need one. Ten, okay so the 10 is actually your slope which is represented by the m in the equation. So guess what, it goes in here, 10t okay? 
So the relationship between the degree Celsius right here versus the time is just that the degree, the temperature is equal to 10 times the t, that's it. So the equation here, the equation for that relationship is right over here. You can either use this one right here or feel free to go y equals to 10 times the x. You can also use this equation, okay? Oh, where did it go? 
Y equals to 10 times the x, okay? So that way, it's easier. All right, but if you want to use the variables from the question, then it will be the degree Celsius equals the 10 times the t. All right? Let's check on the next--

We will learn how to plot linear equations, and then use the graphs as an aid to answer questions about the linear relations. Alternatively, we can find out the linear equations from their graphs. In addition, we will learn how to plot graphs and determine their equations when we are given the table of values of linear relations. We will also explore the concepts of interpolating and extrapolating data from graphs of linear equations.  