Intro W4

•      Intro W4

  •  Objectives

    1. The sections for this week are:
       • 4.1 Use the Rectangular Coordinate System
       • 4.2 Graph Linear Equations in Two Variables
       • 4.3 Graph with Intercepts
       • 4.4 Understand Slope of a Line

   

   Intro and Learning Objectives (click on all tabs to see all sections)

  • 4.1
  • 4.2
  • 4.3
  • 4.4

   Learning Outcomes

  In this section, you will:

  • Plot points in a rectangular coordinate system
  • Verify solutions to an equation in two variables
  • Complete a table of solutions to a linear equation
  • Find solutions to a linear equation in two variables

   Intro

  Just like maps use a grid system to identify locations, a grid system is used in algebra to show a relationship between two variables in a rectangular coordinate system. The rectangular coordinate system is also called the xy-plane or the ‘coordinate plane’.

  The horizontal number line is called the x-axis. The vertical number line is called the y-axis. The x-axis and the y-axis together form the rectangular coordinate system. These axes divide a plane into four regions, called quadrants. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise. In the rectangular coordinate system, every point is represented by an ordered pair. The first number in the ordered pair is the x-coordinate of the point, and the second number is the y-coordinate of the point.

   Learning Outcomes

  In this section, you will:

  • Solve coin word problems
  • Solve ticket and stamp word problems
  • Solve mixture word problems
  • Use the mixture model to solve investment problems using simple interest

   Intro

  In the previous section, we found several solutions to the equation 3x+2y=6. We can plot these solutions in the rectangular coordinate system as shown 

  

  Notice how the points line up perfectly? We connect the points with a line to get the graph of the equation

  

  Every point on the line is a solution of the equation. Also, every solution of this equation is a point on this line. Points not on the line are not solutions.

   Learning Outcomes

  In this section, you will:

  • Identify the x - and y - intercepts on a graph
  • Find the x - and y - intercepts from an equation of a line
  • Graph a line using the intercepts

   Intro

  Every linear equation can be represented by a unique line that shows all the solutions of the equation. We have seen that when graphing a line by plotting points, you can use any three solutions to graph. This means that two people graphing the line might use different sets of three points.

  At first glance, their two lines might not appear to be the same, since they would have different points labeled. But if all the work was done correctly, the lines should be exactly the same. One way to recognize that they are indeed the same line is to look at where the line crosses the x- axis and the y- axis. These points are called the intercepts of the line.

   Learning Outcomes

  In this section, you will:

  • Use geoboards to model slope
  • Use $m=\frac{rise}{run}$ to find the slope of a line from its graph
  • Find the slope of horizontal and vertical lines
  • Use the slope formula to find the slope of a line between two points
  • Graph a line given a point and the slope
  • Solve slope applications

   Intro

  When you graph linear equations, you may notice that some lines tilt up as they go from left to right and some lines tilt down. Some lines are very steep and some lines are flatter. What determines whether a line tilts up or down or if it is steep or flat?

  In mathematics, the ‘tilt’ of a line is called the slope of the line. The concept of slope has many applications in the real world. The pitch of a roof, grade of a highway, and a ramp for a wheelchair are some examples where you literally see slopes. And when you ride a bicycle, you feel the slope as you pump uphill or coast downhill.

  In this section, we will explore the concept of slope.

   Readings

  1. Text: Read the sections from Openstax book Links to an external site. (Links to an external site.)
  2. Videos: Watch all the videos from "Resources W4"

   Assignments

  • Take Notes Week 4  These are the notes for all sections we cover in Week X.          Due Friday night.
    Directions: Each section is accompanied by a Handout. Each Handout contains a few definitions, a few "How To" explanations, examples, and "Try It" exercises. Using the structure of the handout you have to write your own notes. Your notes must contain:

  • • Your name
    • The name of the section
    • Definitions and "How To" from the provided handout (this is optional, however, it will be a good idea to have the complete notes)
    • Everywhere there is a "Read Ex nr..." you have to read the example from the ebook and write in your notes : "I read the Ex nr..." . The link for the section in the ebook is provided at the bottom of the page.
    • You have to solve ALL "Try It" exercises.

  After you complete your notes you have to submit them. See Take Notes Methods. 

   

  • Video quizzes Week 4          Due Saturday night 11:59pm

  • • To learn the material for this sections, take notes while watching each video and then demonstrate what you learned by doing the exercise below it.

   

  • Homework Week  4              Due Sunday night 11:59pm. 
    
    • There are 5 Homework this week. This are online Homework but you do not have to leave Canvas. Just click on each link, answer the questions, and came back for the next section. There is no partial credit, each question is either 100% good or not. However you have unlimited attempts for each question. A 5% per day penalty applies for Late work if you'll do it until Tuesday night. After that the Homework will be open only for practice.

   

  • Exam 2. 

    Exam 2 will assess your knowledge of Chapter 2 and 3. Be sure you have completed the Reading/Video Assignments as well as the Homework Assignments for these sections before you attempt the exam.

    The Homework assignments in particular will prepare you to do well on the exam, not only because they will help you master the material, but also because you will be familiar with entering answers in a way that can be read by the software. Be sure to use the same entry methods you used on the homework for notation, graphing, and equation-writing on this quiz.

    Resources

    Things You May Use for this exam: hand-written notes, calculator, scratch paper, writing implement, eraser.

    Things you may NOT use for this quiz: other people, anything else on your phone, anything else on your computer, anything not mentioned in the list of Things You May Use. I recommend that you put your phone away (or in airplane mode if you’re using it as a calculator) so it doesn’t distract you.

    If you have questions on the exam, please send me an Inbox message right away.

    Exam Settings

    • The 48-hour exam window opens Friday morning and closes Saturday night. I recommend that you not wait until the last hour to take the test as servers can get busy then. 
    • You will have one attempt on this exam. 
    • The time limit is 120 minutes, which must be completed before the deadline on Sunday at midnight.

   

  THE DUE DATES FOR ASSIGNMENTS ARE FRIDAY SATURDAY AND SUNDAY. HOWEVER YOU CAN SUBMIT THEM UNTIL TUESDAY NEXT WEEK.

  A 5% per day penalty applies for Late work if you'll do it until Tuesday night. After that the Homework will be open only for practice.