Common Core Standard: Preparation for 8.EE.8b in Lesson 5.2.4 What is a solution to an equation? What does it look like? What is the growth pattern? What is the y intercept? CPM Materials modified by Mr. Deyo
Title: IM8 Ch. 5.1.1 How Can I Change It To y=mx+b Form? Date: Learning Target By the end of the period, I will solve twovariable linear equations for one variable and rewrite linear equations in y = mx + b form. I will demonstrate this by completing Four Square notes and by solving problems in a pair/group activity.
Home Work: Sec. 5.1.1 Desc. Date Due Review & Preview 2 Problems: 5 6, 5 7
Vocabulary 1) growth factor 2) y intercept 3) solve (for a variable) 4) linear equation
5.1.1 How Can I Change It To y = mx + b Form? So far in this course, you have used your Equation Mat and/or symbols to find solutions for all types of linear equations with one variable. Today you will learn how to apply these skills to solving linear equations with two variables. As you work today, keep these questions in mind: By the end of this lesson, you should be able to answer the following target questions: What is a solution to an equation? What does it look like? What is the growth pattern? What is the y intercept?
5 1 You now have a lot of experience working with equations that compare two quantities. For example, while working with the height of a tree, you found the relationship y = 4x + 5, which compared x (the number of years after it was planted) with y (its height in feet). Use the equation for this tree to answer the questions below. What was its starting height? How can you tell from the equation? What was its growth rate? (That is, how many feet did the tree grow per year?) Justify your answer.
http://www.cpm.org/technology/general/tiles/? tiledata=bhcc3%205 2b cla2x boy aajqvqhajrmq1abpvtqaas5ssaasetv aar9svaarituabqfsjauwlppauwcqwauwnrfauw4qwauxjp9auxqpvaux5qmauxprra uyvqnauygrthf5 2b o9o9 IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook 5 2a&c CHANGING FORMS You can find the growth rate and starting value for y = 4x + 5 quickly, because the equation is in y = mx + b form. But what if the equation is in a different form? Explore this situation below using 5 2b tiles (CPM). a) The line 6x + 2y = 10 is written in standard form. Can you tell what the growth of the line is? Its y intercept? Predict these values. growth = y intercept = b) The equation 6x + 2y = 10 is shown on the Equation Mat on the next page. Set up this equation on your Equation Mat using tiles. Using only legal moves, rearrange the tiles to get y by itself on the left side of the mat. Record each of your moves algebraically.
http://www.cpm.org/technology/general/tiles/? tiledata=bhcc3%205 2b cla2x boy aajqvqhajrmq1abpvtqaas5ssaasetv aar9svaarituabqfsjauwlppauwcqwauwnrfauw4qwauxjp9auxqpvaux5qmauxprra uyvqnauygrthf5 2b o9o9 IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook 6x + 2y = 10 5 2b&c CHANGING FORMS Using only legal moves, rearrange the tiles to get y by itself on the left side of the mat. Record each of your moves algebraically. c) Now use your result from part (b) to find the growth pattern and y intercept of the line 6x + 2y = 10. Did your result match your prediction in part (a)?
2x + y = 3x 7 5 3a Draw & rearrange your tiles to create an equation that starts with y = Be sure to record all of your moves algebraically and be prepared to share your steps with the class. What is the pattern of growth for your line? What is the y intercept? How can you tell? growth = y intercept =
x + 2y = 3x + 4 5 3b Draw & rearrange your tiles to create an equation that starts with y = Be sure to record all of your moves algebraically and be prepared to share your steps with the class. What is the pattern of growth for your line? What is the y intercept? How can you tell? growth = y intercept =
2(y 3) = 2x 6 5 3d Draw & rearrange your tiles to create an equation that starts with y = Be sure to record all of your moves algebraically and be prepared to share your steps with the class. What is the pattern of growth for your line? What is the y intercept? growth = y intercept =
5 3(x + 1) = 2y 3x + 2 5 3e Draw & rearrange your tiles to create an equation that starts with y = Be sure to record all of your moves algebraically and be prepared to share your steps with the class. What is the pattern of growth for your line? What is the y intercept? growth = y intercept =
x (y + 2) = 2(2x + 1) 5 3f Draw & rearrange your tiles to create an equation that starts with y = Be sure to record all of your moves algebraically and be prepared to share your steps with the class. What is the pattern of growth for your line? What is the y intercept? growth = y intercept =
5 4a Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 2(y 3) = 4 Solve for y
5 4b Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 2x + 5y = 10 Solve for x
5 4c Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 6x + 3y = 4y + 11 Solve for y
5 4d Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. Solve for x 3(2x + 4) = 2 + 6x + 10
5 4e Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. y = 3x + 6 Solve for x
5 4f Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. Solve for p m = 8 2(p m)
5 4g Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 4(q 8) = 7q + 5 Solve for q
5 4h Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. Solve for y x 2 + 4y = 2(3x 6 x) + x 2
5 5 A tile pattern has 5 tiles in Figure 0 and adds 7 tiles in each new figure. Write the equation of the line that represents the growth of this pattern. Graph the equation and draw a growth triangle for the line. http://homework chapter/ch5/les Graph What is the rule? y = ( )x + ( ) How many tiles in Figure 0? Where's the y intercept? (, ) Describe the pattern:
5 6a Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 2x + 22 = 12 Solve for x
5 6b Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 2x y = 3 Solve for y
5 6c Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 2x + 15 = 2x 15 Solve for x
5 6d Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 6x + 2y = 10 Solve for y
5 7 Solve each of the following equations for x. Then check each solution. a) x = 7 16 10 b) 6 3 = 15 x c) 2x 12 = 5 8 d) 8 2 = 1 x
5 8 Graph the lines y = 4x + 3 and y = x 7 on the same set of axes. Then find their point of intersection. Graph y = 4x + 3 y intercept: rate of growth: y intercept: rate of growth: y = 1x 7 Where do the two lines intersect? http://homework.cpm. https://www.desmos.com/c chapter/ch5/lesson/5 ( 0, ) ( 0, ) (, )
5 9 Draw Figures 0, 1, 2, and 3 for a tile pattern that could be described by: y = 3x + 10 http://homework.cpm.org chapter/ch5/lesson/5.1.1 Draw the 0 figure. Draw the 1 st figure. Draw the 2 nd figure. Draw the 3 rd figure.