im 8 ch 5.1.1 how can i change it to y=mx+b...
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IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
CPM Materials modified by Mr. Deyo
What is a solution to an equation?
What does it look like?
What is the growth pattern?
What is the yintercept?
Common Core Standard: Preparation for 8.EE.8b in Lesson 5.2.4
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
By the end of the period, I will solve two‐variable 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.
Learning TargetTitle: IM8 ‑ Ch. 5.1.1 How Can I Change It To y=mx+b Form? Date:
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Home Work: Sec. 5.1.1Desc. Date Due
Review & Preview
2 Problems: 5‑6, 5‑7
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Vocabulary1) growth factor
2) yintercept
3) solve (for a variable)
4) linear equation
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
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 yintercept?
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
51 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.
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
52a&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 52b tiles (CPM).
a) The line −6x + 2y = 10 is written in standard form. Can you tell what the growth of the line is? Its yintercept? Predict these values.growth = yintercept =
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%2052b____cLa2x__boy__aajqvqhajrMq1abpVtqaas5sSaasEtvaar9sVaarItuabqfsJauwlpPauwcqwauwnrfauw4qWauxjp9auxQpvaux5qMauxPrrauyVqNauyGrthF52b__o9o9
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
52b&c CHANGING FORMS
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
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.
−6x + 2y = 10
http://www.cpm.org/technology/general/tiles/?tiledata=bHCC3%2052b____cLa2x__boy__aajqvqhajrMq1abpVtqaas5sSaasEtvaar9sVaarItuabqfsJauwlpPauwcqwauwnrfauw4qWauxjp9auxQpvaux5qMauxPrrauyVqNauyGrthF52b__o9o9
c) Now use your result from part (b) to find the growth pattern and yintercept of the line −6x + 2y = 10. Did your result match your prediction in part (a)?
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
53a 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.
2x + y = 3x − 7
What is the pattern of growth for your line? What is the yintercept? growth = yintercept =
How can you tell?
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
53b 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.
x + 2y = 3x + 4
What is the pattern of growth for your line? What is the yintercept? growth = yintercept =
How can you tell?
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
53d 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.
2(y − 3) = 2x − 6
What is the pattern of growth for your line? What is the yintercept? growth = yintercept =
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
53e 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.
5 − 3(x + 1) = 2y − 3x + 2
What is the pattern of growth for your line? What is the yintercept? growth = yintercept =
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
53f 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.
x − (y + 2) = 2(2x + 1)
What is the pattern of growth for your line? What is the yintercept? growth = yintercept =
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
54a 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
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
54b 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
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
54c 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
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
54d Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically.
3(2x + 4) = 2 + 6x + 10
Solve for x
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
54e 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
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
54f Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically.
m = 8 − 2(p − m)
Solve for p
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
54g 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
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
54h Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically.
x2 + 4y = 2(3x − 6 − x) + x2
Solve for y
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
55 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.
What is the rule? y = ( )x + ( )
How many tiles in Figure 0?
Graph
Where's the yintercept?
( , )Describe the pattern:
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch5/lesson/5.1.1/problem/55
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
56a 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
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
56b 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
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
56c 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
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative Inverse
56d 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
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
a)
c)
57 Solve each of the following equations for x. Then check each solution.
x 716 10
b)
d)
6 315 x
8 2 1 x
2x 12 5 8
=
=
=
=
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
58 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
Where do the two lines intersect?
yintercept:
https://www.desmos.com/calculator/v5sjsui72qhttp://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch5/lesson/5.1.1/problem/58
y = 1x 7
( , )
( 0 , )
( 0 , )yintercept:
rate of growth:
rate of growth:
IM 8 Ch 5.1.1 How Can I Change It to y=mx+b Form.notebook
Draw the 0 figure.
Draw the 1st figure.
59
Draw the 2nd figure.
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch5/lesson/5.1.1/problem/59Draw Figures 0, 1, 2, and 3 for a tile pattern that
could be described by: y = −3x + 10
Draw the 3rd figure.