Writing linear equations notes

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# Writing linear equations notes

My district is moving to a standards based curriculum, and has identified priority standards for every course. These are the standards we are required to address and assess our students over, so they pretty much form our units.

I normally teach year-long courses 47 minute classes per day. However, due to a lot of district specific things involving SPED students, a new course introduction, and graduation requirements, this year I taught a block course 94 minute classes per day of Foundations of Algebra first semester, which covered skill gaps students would need to find success in Algebra 1.

This semester, I am teaching most of those same students Algebra 1 on a block schedule. This means I get to start Algebra 1 from the beginning in the same year and revise my activities and INB pages! Unit 1. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

I was excited for this opportunity to change a lot of the pages and see if I got better results. Partners split the Function Auction sheet between them, and each student chose 3 examples and 3 non examples to glue in. Skill 2: I can find the slope, y-intercept, and x-intercept of a linear function. I broke slope down into representations: tables, graphs, and situations. We get to equations later. Of course we watched Slope Dude!

The other page addresses intercepts, and I like the way it turned out. The definition boxes on the front come from Sarah Carterand I just combined them with examples on the inside.

Writing Linear Equations: Slope-Intercept Form [fbt]

I love that I made this a separate skill this time. My students did a much better job at recognizing slope-intercept, standard, and point-slope form this time. I would like to add another page here about converting between forms, because although we discussed how to find slope and a point to use to graph directly from each form, my students still struggled a lot with graphing when the equation is in standard form.

I made two nearly identical pages here — one for creating a table of values and graphing, and one for identifying information from the equation like slope and y-intercept and graphing that way.

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All of my students except one abandoned making the tables after we learned the other way, but I think it was worth it to still discuss. We busted out my giant graph made from a bedsheetwhich was really good because it turns out that my students really struggled with graphing ordered pairs, so it was extremely good practice to give each of them a checker and make them graph one of the points from our table!

I almost want to make a THIRD page that is similar to these two that shows how you can get every equation into slope-intercept form and graph that way. Anyone else think that would be helpful? Here you can see my intense scaffolding, especially when you compare it to similar skill based pages from the first time I taught this skill this year. My students in my year long Algebra 1 got so incredibly overwhelmed by all the steps define variables, choose a form of equation, find the slope and intercept, write the actual equationthat I decided to make EACH STEP a separate page in our notebooks and we also practiced each step separately! If you look at these pages closely, you will see that I used the exact same word problems throughout each step of the process. The change seemed to be effective for them. Skill 6: I can generate all other representations of a linear function when given one representation.

This is always going to be a rough skill, I think.

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So you have to make them all. I did cut the number of examples in their notes down a bit from last go around though I took one of the examples from this file out after I printed them and was more explicit about identifying which representation you were given to start with. I think this skill is a good exercise in thinking systematically, which is a weakness for most of my students. Math teacher at an alternative high school.In the introduction to this section we briefly discussed how a system of differential equations can arise from a population problem in which we keep track of the population of both the prey and the predator.

It makes sense that the number of prey present will affect the number of the predator present. Likewise, the number of predator present will affect the number of prey present. Therefore the differential equation that governs the population of either the prey or the predator should in some way depend on the population of the other. This will lead to two differential equations that must be solved simultaneously in order to determine the population of the prey and the predator.

The whole point of this is to notice that systems of differential equations can arise quite easily from naturally occurring situations. Developing an effective predator-prey system of differential equations is not the subject of this chapter. We are going to be looking at first order, linear systems of differential equations. These terms mean the same thing that they have meant up to this point. The largest derivative anywhere in the system will be a first derivative and all unknown functions and their derivatives will only occur to the first power and will not be multiplied by other unknown functions.

Here is an example of a system of first order, linear differential equations. We will worry about how to go about solving these later. At this point we are only interested in becoming familiar with some of the basics of systems. We can write higher order differential equations as a system with a very simple change of variable.

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Note the use of the differential equation in the second equation. We can also convert the initial conditions over to the new functions. We will call the system in the above example an Initial Value Problem just as we did for differential equations with initial conditions. Systems of differential equations can be converted to matrix form and this is the form that we usually use in solving systems.

In this case we need to be careful with the t 2 in the last equation. The last thing that we need to do in this section is get a bit of terminology out of the way. Starting with. Notes Quick Nav Download.

Go To Notes Practice and Assignment problems are not yet written. As time permits I am working on them, however I don't have the amount of free time that I used to so it will take a while before anything shows up here.Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter?

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## Writing Linear Equations (Day 1 of 2)

English Language Arts. Foreign Language. Social Studies - History. History World History. For All Subject Areas. See All Resource Types.Toggle navigation. Help Preferences Sign up Log in. View by Category Toggle navigation. Products Sold on our sister site CrystalGraphics. Title: Writing and Graphing Linear Equations. Description: Writing and Graphing Linear Equations Linear equations can be used to represent relationships.

Given the slope and y-intercept, write the equation of a line in slope Tags: equations graphing linear solving with writing. Latest Highest Rated. This leads to graphing a linear equation and writing the equation of a line in three different forms. Collinear Points that lie on the same line. Slope A measure of the steepness of a line on a graph rise divided by the run.

All solutions of a particular linear equation fall on the line, and all the points on the line are solutions of the equation. Look at the graph to the left, points 1, 3 and -3, -5 are found on the line and are solutions to the equation.

### Writing Linear Equations

The graph to the right shows an example where each time the x-value increases by 2, the y-value increases by 3. What does Company A charge for 20 minutes of service? Tables can be used to graph linear equations by simply graphing the points from the table. The equation y 2x 3 is a linear equation because it is the graph of a straight line.

Each time x increases by 1 unit, y increases by 2. The following example describes how slope rate of change is applied. Rate of change is also know as grade or pitch, or rise over run. Change is often symbolized in mathematics by a delta for which the symbol is the Greek letter? The graph shows an example where each time the x-value increases by 3, the y-value increases by 2. For a line on the coordinate plane, slope is the following ratio. This ratio is often referred to as rise over run.

To make finding slope easier, find where the line crosses at an x and y junction. Choose two points on the line -4, 4 and 8, Count the rise over run or you can use the slope formula. Notice if you switch x1, y1 and x2, y2you get the same slope 21 Use the graph to find the slope of the line. Slope-intercept form of an equation a linear equation written in the form y mx b, where m represents slope and b represents the y-intercept.

The x-intercept is the x-value of the point where the line crosses. The y-intercept is the y-value of the point where the line crosses. Ax By C 25 To graph a linear equation in standard form, you fine the x-intercept by substituting 0 for y and solving for x.Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter?

All Categories. Grade Level. Resource Type. Log In Join Us. View Wish List View Cart. Results for slope intercept form guided notes Sort by: Relevance. You Selected: Keyword slope intercept form guided notes. Grades PreK. Other Not Grade Specific. Higher Education. Adult Education. Digital Resources for Students Google Apps. Internet Activities. English Language Arts. Foreign Language. Social Studies - History.

History World History. For All Subject Areas. See All Resource Types. Students learn about slope-intercept form in the order below. They will:- Attempt but hopefully not know how to decide if the point ,63 is on a c.

MathAlgebraGraphing. WorksheetsHomeworkScaffolded Notes. Add to cart. Wish List. These guided notes and practice are a perfect way to introduce your middle or high school students to slope intercept form. These notes help organize your student's notes as they are introduced to a new concept. My students very much prefer this method of note taking and have more confidence when ap.

Study GuidesWorksheetsMinilessons. Guided notes on how to write equations from graphs, tables and words.Do you get confused when you have to write linear equations? Don't worry, that's about to change!

In the previous unit, Graphing Equations you learned how to graph linear equations on a coordinate grid.

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In this unit, we are going to reverse that process and write equations to match a graph or a word problem. This unit is very important, because in many real life situations, you will not be given an equation to solve. You will be given a problem, that will require you to first write the equation and then to solve the equation. Click on the lesson below that you need help with, or follow along in order to complete the unit on Writing Equations. The Algebra Class E-course offers video tutorials, tons of practice problems with step-by-step answer keys, and graphic organizers that will guarantee your success in Algebra 1.

We have a new platform with updated videos and worksheets. Click here to login to our Learn Worlds platform. Algebra Class. Need Help? Try This Online Calculator! Let Us Know How we are doing!After about 4 minutes, I will ask volunteers to come to the front of the room to walk the class through their responses to the Do-Now. Then, we will quickly discuss the responses to the old exit cards. Before we begin, I will ask students what word is hidden in the word "linear" and to make a prediction about the meaning of this word.

The primary activity in today's lesson is a group challenge. I begin by telling my students that their challenge is to figure out how many stacked styrofoam cups it would take to reach to the top of my head. Butthey will only be given 4 cups to figure out an answer to this question.

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I will give students a quiet moment to think about the task. Then, I will ask students to think about what information is needed to be able to answer this question.

I will again pause, and after a moment allow students to share their plan of attack to the group. I expect that right away, at least one student will say "We need to know how tall you are Next, I will ask students to predict the height of two stacked cups. Many of my students will immediately double the height of one cup. I expect at least one will announce that it would only take 18 stacked cups to reach the top of my head.

If when this occurs, I will stack 18 cups to show students that that cup tower barely reaches my shin.

At this point students will immediately see that this situation will require more thought than initially anticipated. I will let the class continue to brainstorm aloud for a few more minutes. If the suggestion is not made by a student after a few more minutes, I will prompt students create a table to measure the height of 1, 2, 3, and 4 cups. I will use the questions below to guide the discussion:.

To close our investigation, we will stack the predicted number of cups to visually test if the function that my students found is correct. Students will copy slope intercept form inside of the box on the middle section of their Guided Notes. I will ask students to help me create a list underneath each component of the equation.

Eventually the section should look like this. We will complete Problems 1 and 2 as a whole group so that I can model the exact type of thinking and reasoning needed to interpret a linear situation. Students will work in pairs on the rest of the problems until the end of class. We will check back in every 10 minutes or so to review the responses to a few problems at a time. The most common issue that I see when my students work on these problems is that they answer questions with the words "input" and "output", and not in terms of what is happening in the context of the problem.

I have found that the best way of combating this misconception is through continued practice. To help students who are still struggling, I will prompt them to make a table of values for each, and to use the headings of the table to interpret the meaning of the situation.

I will ask students to decide if these functions are the same, and if the order of the numbers is important.  