Subjects

Algebra 1

Slope

Learn How to Find Slope and Use Point-Slope Form and Slope-Intercept Form

Name: Knowunity
Brand: Knowunity

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Learn How to Find Slope and Use Point-Slope Form and Slope-Intercept Form

Maithy Smith

@maithysmith

64 Followers

This lesson covers key concepts in linear algebra, focusing on slope calculations and equation forms. Students will learn how to find slope using two points, understanding point-slope form equations, and converting point-slope form to slope-intercept form. The material progresses from basic slope calculations to more complex equation manipulations, providing a solid foundation for linear algebra concepts.

Key points:

Slope calculation using the "rise over run" formula
Finding slope from two given points
Using point-slope form to create linear equations
Converting between point-slope and slope-intercept forms
Practical applications of linear equations

5/24/2023

152

Rate of Change OR Slope
Slope is the ratio
horizontal
rise
run
Rate of
of change
"rise over run"
M=
Example 2:
Example 3:
Finding Slope from

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Point-Slope Form of an Equation

This page delves into the point-slope form of linear equations, providing a detailed explanation of its structure and application.

Definition: The point-slope form of a linear equation is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

The document outlines two scenarios for using point-slope form:

When given a point (x₁, y₁) and a slope (m)
When given two points: (x₁, y₁) and (x₂, y₂)

Example: For the point (4,1) and slope 2, the point-slope form equation is y - 1 = 2(x - 4)

The page provides a step-by-step process for creating and solving point-slope form equations:

Label the ordered pair(s)
Identify or calculate the slope
Substitute values into the point-slope form
Convert to slope-intercept form (y = mx + b)

Highlight: Converting point-slope form to slope-intercept form is an essential skill for graphing linear equations.

The document includes two detailed examples, demonstrating how to work with different sets of points and slopes to create and manipulate point-slope form equations.

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Practice Problems and Notes

This page offers a series of practice problems to reinforce the concepts of slope calculation and point-slope form equations.

The problems cover various scenarios:

Given a point and slope, write the equation in point-slope form and convert to slope-intercept form
Given two points, find the slope and write the equation in both point-slope and slope-intercept forms
Apply the concepts to a real-world situation involving temperature change over time

Example: For the point (0, -9) and slope 4, the solution progresses from y + 9 = 4(x - 0) to y = 4x + 9

The page provides step-by-step solutions for each problem, demonstrating the process of: • Identifying given information • Calculating slope when necessary • Writing equations in point-slope form • Converting equations to slope-intercept form

Highlight: Practice problems help solidify understanding of how to find slope using two points and how to apply this knowledge to create and manipulate linear equations.

The final problem presents a real-world application, asking students to model the temperature change in a pond over time using a linear equation. This demonstrates the practical utility of understanding slope and linear equations in scientific contexts.

View

Rate of Change or Slope

This page introduces the concept of slope as a rate of change in mathematics. It explains various ways to express and calculate slope, focusing on the "rise over run" method.

Definition: Slope is the ratio of a line's vertical change compared to its horizontal change.

The page presents multiple representations of slope: • As a ratio of rise to run • As "change in y over change in x" • Using the mathematical formula m = Δy / Δx

Vocabulary: Rise refers to the vertical change, while run refers to the horizontal change.

The document then provides a step-by-step guide for finding slope using two points:

Label the first ordered pair as (x₁, y₁)
Label the second ordered pair as (x₂, y₂)
Substitute values into the slope formula and solve

Example: For points (4,4) and (0,1), the slope is calculated as m = (1-4) / (0-4) = -3/4

The page concludes with two more examples, demonstrating how to calculate slope for different sets of points, including cases resulting in negative slopes.

Highlight: Understanding how to calculate slope is crucial for analyzing linear relationships and graphing lines.

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Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

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Knowunity is the # 1 ranked education app in five European countries

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Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

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I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

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The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

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Subjects

Algebra 1

Slope

Learn How to Find Slope and Use Point-Slope Form and Slope-Intercept Form

Maithy Smith

@maithysmith

64 Followers

Key points:

Slope calculation using the "rise over run" formula
Finding slope from two given points
Using point-slope form to create linear equations
Converting between point-slope and slope-intercept forms
Practical applications of linear equations

5/24/2023

152

9th/8th

Algebra 1

Point-Slope Form of an Equation

This page delves into the point-slope form of linear equations, providing a detailed explanation of its structure and application.

Definition: The point-slope form of a linear equation is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

The document outlines two scenarios for using point-slope form:

When given a point (x₁, y₁) and a slope (m)
When given two points: (x₁, y₁) and (x₂, y₂)

Example: For the point (4,1) and slope 2, the point-slope form equation is y - 1 = 2(x - 4)

The page provides a step-by-step process for creating and solving point-slope form equations:

Label the ordered pair(s)
Identify or calculate the slope
Substitute values into the point-slope form
Convert to slope-intercept form (y = mx + b)

Highlight: Converting point-slope form to slope-intercept form is an essential skill for graphing linear equations.

The document includes two detailed examples, demonstrating how to work with different sets of points and slopes to create and manipulate point-slope form equations.

Practice Problems and Notes

This page offers a series of practice problems to reinforce the concepts of slope calculation and point-slope form equations.

The problems cover various scenarios:

Given a point and slope, write the equation in point-slope form and convert to slope-intercept form
Given two points, find the slope and write the equation in both point-slope and slope-intercept forms
Apply the concepts to a real-world situation involving temperature change over time

Example: For the point (0, -9) and slope 4, the solution progresses from y + 9 = 4(x - 0) to y = 4x + 9

Highlight: Practice problems help solidify understanding of how to find slope using two points and how to apply this knowledge to create and manipulate linear equations.

Rate of Change or Slope

This page introduces the concept of slope as a rate of change in mathematics. It explains various ways to express and calculate slope, focusing on the "rise over run" method.

Definition: Slope is the ratio of a line's vertical change compared to its horizontal change.

The page presents multiple representations of slope: • As a ratio of rise to run • As "change in y over change in x" • Using the mathematical formula m = Δy / Δx

Vocabulary: Rise refers to the vertical change, while run refers to the horizontal change.

The document then provides a step-by-step guide for finding slope using two points:

Label the first ordered pair as (x₁, y₁)
Label the second ordered pair as (x₂, y₂)
Substitute values into the slope formula and solve

Example: For points (4,4) and (0,1), the slope is calculated as m = (1-4) / (0-4) = -3/4

The page concludes with two more examples, demonstrating how to calculate slope for different sets of points, including cases resulting in negative slopes.

Highlight: Understanding how to calculate slope is crucial for analyzing linear relationships and graphing lines.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Learn How to Find Slope and Use Point-Slope Form and Slope-Intercept Form

Point-Slope Form of an Equation

Practice Problems and Notes

Rate of Change or Slope

Similar Content

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

15 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying

Learn How to Find Slope and Use Point-Slope Form and Slope-Intercept Form

Point-Slope Form of an Equation

Practice Problems and Notes

Rate of Change or Slope

Similar Content

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

15 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying