Subjects

Careers

Open the App

Subjects

Super Easy Slope-Intercept and Point-Slope Math Notes PDF

Open

92

0

user profile picture

Violet P

9/23/2023

Algebra 1

Everything you need to know

Subjects

/

Algebra 1

/

Slope Intercept & Standard Form

/

Standard Form

/

Graphing a Linear Equation: 5X+2Y=20

Super Easy Slope-Intercept and Point-Slope Math Notes PDF

This comprehensive guide covers essential concepts in algebra, focusing on linear equations, inequalities, and various forms of representing functions. It provides in-depth explanations and examples for slope-intercept form, point-slope form, and other key mathematical concepts.

• The guide covers functions, zero of functions, and different equation forms
• It explains slope calculations, including zero and undefined slopes
• The document includes formulas for midpoint, systems of equations, and exponential functions
• Advanced topics like factoring, exponent rules, and scientific notation are also covered

...

9/23/2023

690

Math & Overview - Function= f(x)=√x+C ⇒ F(*= 2x+3; F= 3 ⇒ f (3)=2(3)+3 e this function function number Zero of function = f(x) = 0 + 0 = 2x+

View

Advanced Algebraic Concepts and Graphing

This page delves deeper into algebraic concepts, focusing on graphing linear inequalities, exponential functions, and more advanced topics in algebra.

The section on graphing linear inequalities explains how to use the y = mx + b form to graph inequalities. It provides an example and important notes:

Example: To graph x - y ≤ 4, rearrange it to y ≥ -4 + x.

Highlight: When multiplying or dividing an inequality by a negative number, the inequality sign flips.

The page introduces exponential functions in the form y = a·bˣ, explaining that if b > 1, the function will increase. It also covers exponential growth and geometric sequences.

Definition: Exponential growth is represented by the formula y = a1+r1+rᵗ, where a is the initial amount, r is the rate, and t is time.

The arithmetic sequence formula is presented as aₙ = dn−1n-1 + a, where d is the common difference between terms.

The page then moves on to more advanced topics, including exponent rules, the difference of squares, and FOIL First,Outer,Inner,LastFirst, Outer, Inner, Last method for multiplying binomials.

Example: Using FOIL to multiply x+2x+2x+3x+3 = x² + 5x + 6

Factoring trinomials is explained, including the "slip and slide" method for trinomials with a coefficient on x².

The page concludes with a brief explanation of scientific notation, showing how to convert numbers to and from this format.

Vocabulary: Scientific notation is expressed as A × 10ⁿ, where 1 ≤ |A| < 10 and n is an integer.

This page provides a wealth of information on advanced algebraic concepts, building upon the foundations laid in the previous page.

Similar Content

Know Linear Equations and Graphs thumbnail

14

280

9th/10th

Linear Equations and Graphs

These notes explain the basics of linear equations, isolating variables, translating word problems into equations, calculating slopes, etc.

Know Solving leaner equations thumbnail

9

159

Solving leaner equations

About the topic

Know Functions thumbnail

22

455

Functions

Notes that were taken in an Algebra 1 class.

Know Algebra 1 EOC quick notes thumbnail

47

432

9th/8th

Algebra 1 EOC quick notes

These notes have concepts and information from topics from Algebra 1.

Know equations summary thumbnail

6

54

9th

equations summary

notes on equations

Know Function Notation thumbnail

4

124

9th/7th

Function Notation

My teacher's slide show on function notation

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.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

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

4.9+

Average App Rating

21 M

Students use Knowunity

#1

In Education App Charts in 17 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

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

Subjects

Algebra 1

Slope Intercept & Standard Form

Standard Form

Graphing a Linear Equation: 5X+2Y=20

 

Algebra 1

•

690

•

Sep 23, 2023

•

2 pages

Super Easy Slope-Intercept and Point-Slope Math Notes PDF

user profile picture

Violet P

@ruta_sepepsi

This comprehensive guide covers essential concepts in algebra, focusing on linear equations, inequalities, and various forms of representing functions. It provides in-depth explanations and examples for slope-intercept form, point-slope form, and other key mathematical concepts.

• The guide... Show more

Math & Overview - Function= f(x)=√x+C ⇒ F(*= 2x+3; F= 3 ⇒ f (3)=2(3)+3 e this function function number Zero of function = f(x) = 0 + 0 = 2x+

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Advanced Algebraic Concepts and Graphing

This page delves deeper into algebraic concepts, focusing on graphing linear inequalities, exponential functions, and more advanced topics in algebra.

The section on graphing linear inequalities explains how to use the y = mx + b form to graph inequalities. It provides an example and important notes:

Example: To graph x - y ≤ 4, rearrange it to y ≥ -4 + x.

Highlight: When multiplying or dividing an inequality by a negative number, the inequality sign flips.

The page introduces exponential functions in the form y = a·bˣ, explaining that if b > 1, the function will increase. It also covers exponential growth and geometric sequences.

Definition: Exponential growth is represented by the formula y = a1+r1+rᵗ, where a is the initial amount, r is the rate, and t is time.

The arithmetic sequence formula is presented as aₙ = dn−1n-1 + a, where d is the common difference between terms.

The page then moves on to more advanced topics, including exponent rules, the difference of squares, and FOIL First,Outer,Inner,LastFirst, Outer, Inner, Last method for multiplying binomials.

Example: Using FOIL to multiply x+2x+2x+3x+3 = x² + 5x + 6

Factoring trinomials is explained, including the "slip and slide" method for trinomials with a coefficient on x².

The page concludes with a brief explanation of scientific notation, showing how to convert numbers to and from this format.

Vocabulary: Scientific notation is expressed as A × 10ⁿ, where 1 ≤ |A| < 10 and n is an integer.

This page provides a wealth of information on advanced algebraic concepts, building upon the foundations laid in the previous page.

Math & Overview - Function= f(x)=√x+C ⇒ F(*= 2x+3; F= 3 ⇒ f (3)=2(3)+3 e this function function number Zero of function = f(x) = 0 + 0 = 2x+

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Math Overview and Linear Equations

This page provides a comprehensive overview of fundamental algebraic concepts, focusing on linear equations and their various forms. It covers essential topics that form the backbone of algebra and graphing.

The page begins by introducing functions and their notations. It then delves into the concept of zero of a function, which is crucial for understanding the behavior of equations.

Definition: A zero of a function is the value of x that makes the function equal to zero, i.e., fxx = 0.

The slope-intercept form of a linear equation is introduced as y = mx + b, where m represents the slope and b represents the y-intercept. This form is particularly useful for graphing linear equations quickly.

Highlight: The slope-intercept form y=mx+by = mx + b is one of the most commonly used forms for linear equations, making it easy to identify the slope and y-intercept at a glance.

The page also covers the point-slope form of a linear equation, which is useful when you know a point on the line and its slope. An example is provided to illustrate how to use this form:

Example: Given a point 4,54,5 and a slope of 6, the point-slope form equation would be y - 5 = 6x−4x - 4.

The slope formula is introduced as y2−y1y₂ - y₁ / x2−x1x₂ - x₁, which is used to find the slope between two points. The page also explains special cases of slopes:

Vocabulary:

  • Zero slope: When the top number yy in the slope fraction is zero.
  • Undefined slope: When the bottom number xx in the slope fraction is zero.

The concepts of domain and range are briefly mentioned, along with the midpoint formula. The page concludes with an introduction to systems of equations and methods for solving them, including substitution, elimination, and graphing.

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

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user