Linear Equations

By:
 Aiyanna 

Table of Contents:

Chapter 1: Formulas
Examples: (Point-Slope Form)
Videos to Help

Chapter 2: Writing linear equations
Example of a Graph

Chapter 3: Equations in Standard form
Examples

Chapter 4: A Point and Slope
Examples:

Chapter 5: Types of Lines
Examples:

Introduction

Chapter 1: Formulas
Examples: (Point-Slope Form)
Videos to Help

Chapter 2: Writing linear equations
Example of a Graph

Chapter 3: Equations in Standard form
Examples

Chapter 4: A Point and Slope
Examples:

Chapter 5: Types of Lines
Examples:

There are many different formulas we can use for Linear Equations.

In these chapters you will learn the different types of equations you can use for Linear Equations and how they can be used in other Units of Math.

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Chapter 1:

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Formulas!

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Slope-Intercept Formula:

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What is it used for?

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The slope-Intercept form is used to represent the slope of a line.

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The Formula

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y = mx + b

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What do the variables mean?

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M=slope
B=y-intercept

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Point-Slope Formula

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What is it used for?

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The point-Slope Formula is used to write an equation of a line passing through a point on a graph.

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The Formula

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y-y1= m(x-x1) 

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Slope Intercept Form Rap

Review of slope + Slope-intercept Form

Linear Equations in Point-Slope Form

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Slope Formula

What is it used for?

The slope formula is used to find the slope of a line using two coordinates on a graph.

The Formula

How to use the formula:

You must take both y1 and y2 coordinates and divide them by the x1 and x2 coordinates.

Video to help understand

Steps to Solve:

Step 1: Replace the variables y1 and x1 with the X and Y coordinates.

The Formula- y-y1= m( x- x1)
Example:(4,8); Slope = 1
#1. Replace variables with x and y values

y - 8 = 1(x - 4)

Step 2: Use the Distributive Property

Example:
y - 8 = 1(x - 4)
#2. Distribute 1 (The Slope) to x and -4

y - 8 = x - 4

Step 3: Solve for y

Example:
y - 8 = x - 4
#3. Isolate y (in this case you would add 8 + (-4) and get a positive 4)

Answer: y=x+4

Example Problems: (Point-Slope Form)

#1.
(5,6); Slope = 2

#3.
(2,4); Slope = 1

#5.
(1,3); Slope = 1/2

#7.
(3,1); Slope = 4

#9.
(8,2); Slope = 3

#2.
(3,6); Slope = 5

#4.
(7,2); Slope = 7

#6.
(8,4); Slope = 1/2

#8.
(6,5); Slope = 1


#10.
(4,0); Slope = 1

Example Problems: (Point-Slope Form)

#1.
(5,6); Slope = 2

#3.
(2,4); Slope = 1

#5.
(1,3); Slope = 1/2

#7.
(3,1); Slope = 4

#9.
(8,2); Slope = 3

#2.
(3,6); Slope = 5

#4.
(7,2); Slope = 7

#6.
(8,4); Slope = 1/2

#8.
(6,5); Slope = 1


#10.
(4,0); Slope = 1

Answers: Odds

(The Formula.... y - y1 = m(x-x1))

#1. (5,6); Slope = 2
y - 6 = 2(x - 5)
(Distribute m)
y - 6 = 2x - 10
+6 +6
y = 2x - 4

#3. (2,4); Slope = 1
y - 4 = 1(x - 2)
(Distribute m)
y - 4 = x - 2
+4 +4
y = x + 2

#5. (1,3); Slope = 1/2
y - 3 = 1/2(x - 1)
(Distribute m)
y - 3 = 1/2x - 1/2
+3 +3
y = 1/2x + 5/2

#7. (3,1); Slope = 4
y - 1 = 4(x -3)
(Distribute m)
y - 1 = 4x -12
+1 +1
y = 4x - 11

#9. (8,2); Slope = 3
y - 2 = 3(x - 8)
(Distribute m)
y - 2 = 3x - 24
+2 +2
y = 3x - 22

#2. (3,6); Slope = 5
y - 6 = 5(x - 3)
(Distribute m)
y - 6 = 5x - 15
+6 +6
y = 5x - 9

#4. (7,2); Slope = 7
y - 2 = 7(x - 7)
(Distribute m)
y - 2 = 7x - 49
+ 2 +2
y = 7x - 47

#6. (8,4); Slope = 1/2
y - 4 = 1/2(x - 8)
(Distribute m)
y - 4 = 1/2x - 4
+4 +4
y = 1/2x + 8

#8. (6,5); Slope = 1
y - 5 = 1(x - 6)
(Distribute m)
y - 5 = x - 6
+5 +5
y = x - 1

#10. (4, 0); Slope = 1
y - 0 = 1(x - 4)
(Distribute m)
y = x - 4