WEEK 1-INTRODUCTION-TO-LINEAR-EQUATIONS

Welcome 9th graders!

Let's begin our adventure to the fascinating world of Math!

A journey soon begin through Math experiences!

Start

Introduction to Linear Equations

Objectives

Start

Solving Linear Equations

Plotting Linear Equations

Forms of the Linear Equation

Applied Problems

Summary

Solving Linear Equations

What is a Linear Equation?

Definition: A linear equation is in the form:ax + b = 0.

Example 1: 2x + 4 = 0 is a linear equation.

Here:

a variable

x is

As long as 2x+4=0 is in the form ax+b=0, the equation is linear.

a and b

are constants.

Solving Linear Equations

They are about finding the unknown in the equation.

For instance: Solve 2x + 3 = 7

Let's see some examples:

Example 2: Three times a number added to 10 equals 25. Find the number.

Example 1: Solve 5x+6=16

x=2

x=5

Plotting Linear Equationsof two Variables

Let's consider a linear equation with two variables x and y:

y=x+1

The values of x and y which satisfy the equation are not unique.

For instance:

satisfy the equation.

x=0, y=1

but also,

satisfy the equation.

x=3, y=4

Finding Possible Solutions of two Variable Linear Equations

In order to solve a linear equation of two variables, give values to one variable and find the other variable

y=x+1

For instance in:

Tip: Usually...

independent variable

x=0, then y=0+1 -> y=1

Set:

x is

x=1, then y=1+1 -> y=2

dependent variable.

x=2, then y=2+1 -> y=3 ...

Two variable linear equations solutions are placed in a table of values.

And that table is plotted on a Cartesian plane.

Let's see some examples:

Example 1: Find some solutions of y=3x-5 and plot them.

Forms of the Linear Equation

The Slope-Intercept Form

Definition: A linear equation in the slope-intercept form is:y=mx+b

Where:

is called the slope

is called the intercept

The Slope m.

Definition: The slope is the rate of change of y (dependent variable) when x is changed.

If (x₁,y₁), (x₂,y₂) are two points on the line, the slope is computed as follows:

Change of y

Change of x

The intercept b.

Definition: The intercept b is the y coordinate at which the line intercepts with the y-axis.

Let's see some examples:

Example 1: A line passes through points (1,3) and (2,4). Find the line equation.

Step 3

Step 1

y=x+2

Step 2

y = (1)x+2

The Line-Point Form

Definition: A linear equation in the line-point form is:y-y₀=m(x-x₀)

Where:

is called the slope

is a point in the line

(x₀,y₀)

Let's see some examples:

Example 2: A line has a slope of 2 and passes through (1,2). Find the line equation.

Step 1

y-2=2(x-1)

Step 2

The Standard Form

Definition: A linear equation in the standard form is:ax+by+c=0

Where:

are constants.

a,b,c

Applied Problems

Try it by Yourself

The table below shows the number of hours worked (x) and the amount earned (y).

Click to see the data.

Find the linear equation that represents the relationship between hours worked and earnings. Express it in: a) Slope-intercept form. b) Standard form.

07:00

Summary

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See you next time

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6TH-INTRODUCTIONTORATIONALNUMBERS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

MATERIAL

It is highly advised to have:

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).

MA.912.AR.2: Write, solve and graph linear equations, functions and inequalities in one and two variables. MA.912.AR.2.1 Given a real-world context, write and solve one-variable multi-step linear equations. MA.912.AR.2.2 Write a linear two-variable equation to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context. ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

Solution

Answer

Step 5

Step 1

Step 3

a) y=15xb) y-15x=0

Step 4

Step 2

b)

a)