Module 5 Assignment

Mathematics 10C: Module 5 11 Assignment

Module 5 Assignment

Lesson 4 Assignment

Math Lab: Linear Forms

You will revisit the “Linear Function Graph” applet you have looked at in previous lessons. This time, you will use it to observe how the familiar slope-intercept equation relates to the possibly less familiar slope-point equation and general equation.

In the “Linear Function Graph” applet, use the sliders to adjust “m” and “b” in “y  mx  b” as shown in the following image.

For example, to create the graph of y  2x  1, move the “m” slider to 2 and the “b” slider to 1. Keep your eye on the equation above the graph to make sure you have the equation you want.

Once you have the equation set up properly in the slope-intercept equation, you can click on one of the other equation types. This will leave you with the same graph, but with a different equation.

Note: This applet shows you the slope-point equation in simplified form.

Part A

Use the graphing applet to create the specified graphs that follow for the slope-intercept equation; then view the graph in both the slope-point form and the general form.

Complete the last two columns in the table for each graph by copying the appropriate equation from the applet. See if you can figure out how the equations in these two columns relate to the points on the corresponding graph. Later in the lesson, you will explore this connection.

Equation / Slope-Intercept Form
y  mx  b / Slope-Point
Form
y – y1  m(x  x1) / General
Form
Ax  By  C  0
y  2x  3
/ m 
b  / Write the equation in
point-slope form. / Write the equation in general form.
y  2x  3
/ m 
b  / Write the equation in
point-slope form. / Write the equation in general form.
y  2x  4
/ m 
b  / Write the equation in
point-slope form. / Write the equation in general form.
y  2x  4
/ m 
b  / Write the equation in
point-slope form. / Write the equation in general form.

Analysis

1. Examine the four graphs in the previous table. What aspects of these graphs remain the same?

Answer:

2. What aspects of all four graphs are different?

Answer:

3. Why do the three different equations give you the same graph?

Answer:

Part B

Equation / Slope-Intercept Form
y  mx  b / Slope-Point
Form
y – y1  m(x  x1) / General
Form
Ax  By  C  0
y  2x  3
/ m 
b  / Write the equation in
point-slope form. / Write the equation in general form.
y  2x  3
/ m 
b  / Write the equation in
point-slope form. / Write the equation in general form.

/ m 
b  / Write the equation in
point-slope form. / Write the equation in general form.

/ m 
b  / Write the equation in
point-slope form. / Write the equation in general form.

Analysis

4. Examine the four graphs in the table. What aspects of these graphs remain the same?

Answer:

5. What aspects of all four graphs are different?

Answer:

6. Why does the general form have different numbers in it when compared with the slope-intercept and slope-point equation?

Answer:

Once you have completed Math Lab: Linear Forms, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.

Work with a partner to answer the following questions. The questions are based on three equations shown in Lesson 4.

1. Do the three equations shown in the lesson represent the same relationship? Explain.

Answer:

2. How could you get one equation from question 1 to look the same as one of the other equations? Choose two equations, and show the steps you would use to convert one into the other.

Answer:

Once you have completed the Share activity, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.

Together with a partner, compare the general form to the other forms of linear functions. Address the following questions:

3. In what ways is the general form different from the other forms? In what ways is the general form similar to the other forms?

Answer:

4. What are the benefits of expressing a linear function in general form?

Answer:

5. Select equations from the tables in Math Lab: Linear Forms to show how you can convert from

a. slope-intercept form to general form

Answer:

b. general form to slope-intercept form

Answer:

Once you have completed the Share activity, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.

Try This

TT 1. a. Linear functions are listed in the following chart. Identify the pairs that are equivalent by rearranging each equation into slope-intercept form. Then determine the slope and the y-intercept.

Linear Relation / Rearrangement / Slope / y-intercept
A.
B.
C. x  4y  4  0
D.
E. x  4y  16  0
F.

b. State the pairs of relations that are equivalent.

Answer:

Go to your textbook now to practise applying the concepts that you have learned. Show work to support your answers. The work may be descriptive or mathematical. You may want to check the solutions in the back of the textbook to make sure you are doing the questions correctly. You may also want to review relevant parts of the lesson as you work through the problems.

Math 10 (McGraw-Hill Ryerson)

TT 2. a. Complete “Check Your Understanding” questions 2.a), 2.d), and 2.f) on page 365.

Answer:

b. Complete “Check Your Understanding” questions 1.b), 1.d), 1.f), 2, 3.a), 3.d), 5.a), and 5.c) on pages 377 and 378.

Answer:

Foundations and Pre-calculus Mathematics 10 (Pearson)

TT 2. a. Complete “Exercises” questions 4.a), 4.f), 9, and 12 on pages 372 and 373.

Answer:

b. Complete “Exercises” questions 4, 6, 12, 18, and 24 on pages 384 and 385.

Answer:

Once you have completed TT 1 and TT 2, save the Lesson 4 Assignment to your course folder. You will return to the Lesson 4 Assignment later in this lesson.

Reflect and Connect

You are required to complete both Part A and Part B.

Part A: Venn Diagram

A Venn diagram can be used as a graphic organizer. A Venn diagram can help you compare and contrast the properties of two different objects or concepts.

· In the circles labelled Object A and Object B, you would write the names of those items that are being compared.

· In the area where the circles overlap, you would include properties that are common to both Object A and Object B.

· In the areas that are unique to one circle, you would include properties of the object that are not properties of the other object. In this way, you can easily visualize the similarities and differences between two objects.

The following image is an example only.

RC 1. Compare and contrast the features of each pair of linear forms by creating Venn diagrams for the following. You can use the Venn Diagram template to complete this question. Remember to attach your completed Venn diagrams to the Lesson 4 Assignment.

a. slope-intercept form vs. general form

b. slope-intercept form vs. slope-point form

Part B: Sequence Graphic Organizer

A graphic organizer allows you to display a sequence of events or a sequence of steps in a procedure. When creating these organizers, you don’t want to have too many or too few steps. If you have too many steps, it may be difficult to remember. If you have too few steps, you may not have enough details in each step.

RC 2. Construct sequence graphic organizers that demonstrate how to convert from one form to another. You can use the Graphic Organizer: Sequence Wizard to complete this question. Remember to attach your completed graphic organizers to the Lesson 4 Assignment.

a. general form to slope-intercept form

b. slope-point form to slope-intercept form

c. slope-intercept form to general form

Once you have completed both Part A and Part B of the Reflect and Connect activity, save the
Lesson 4 Assignment to your course folder. You will submit the Lesson 4 Assignment to your teacher for marks.