1. Proportional relationships Equations (y=kx)
Lesson 4.2.5
Proportional relationships Equations (y=kx)
obj. 7.RP.2b,c

2. Prior Knowledge
We have been learning about proportional relationships in tables, graphs, equations and verbal descriptions. Let’s review our example from yesterday.
There are 3 students at Central High School per 1 student taking Spanish.
𝑦=𝟑𝑥
Have students explain why each representation is proportional.
Point out the constant of proportionality in each representation.

3. Prior Knowledge
Which table is proportional? TABLE A TABLE B
TABLE B

4. Prior Knowledge
Which graph is proportional? GRAPH A GRAPH B
GRAPH B

5. Prior Knowledge
Which equation is in the correct format for a proportional relationship? EQUATION A EQUATION B 𝑦=2.5𝑥 𝑦=3𝑥+6
EQUATION A

6. Today
We are going to spend more time on the equation of a proportional relationship.
y=kx

7. Different variables can be used besides y, k, and x!
We already know that equations in the form of y = kx represent a proportional relationship.
y=kx
Different variables can be used besides y, k, and x!
When dealing with real-world situations, sometimes we use letters that are more meaningful for the independent (quantity) and dependent variables (total), as well as, the constant.

8. You Try!
Identify the constant of proportionality (unit rate) from these equations:
1) y = 6x
2) y = 𝟑 𝟒 x
c = 7.25p
m = 60h
K = 6 2) K = ¾ 3) K = ) K = 60

9. Which equation calculates the total cost for going on any number of rides?k x
Answer: A

10. 5) You Try! y k x

11. y k x

12. 6) You Try!
Case21 Sample y k x

13. Let’s look at writing some equations in the form 𝑦=𝑘𝑥 when given a word problem.
These can be more challenging because you have to use everything you’ve learned about proportional relationships and unit rates to write these equations.

14. Remember: Total = (unit rate) (quantity)
Determine what is given and what still needs to be found and how it all fits into the equation 𝑦 = 𝑘𝑥.
Remember: Total = (unit rate) (quantity) y = k x
Total
Quantity
Lauren reads 360 pages in 12 hours.
a) Write an equation to represent the relationship between pages and hours.
b) Use the equation to determine how many pages Lauren can read in 16 hours.
y = k x
Total = (unit rate) (quantity)
To find unit rate:
K = 𝑦 𝑥
360 = (unit rate) (12)
360 ÷ 12 = 30
y = x
y = 30 x
y = 30(16)
y = 480

15. Remember: Total = (unit rate) (quantity)
Determine what is given and what still needs to be found and how it all fits into the equation 𝑦 = 𝑘𝑥.
Remember: Total = (unit rate) (quantity) y = k x
Total
Quantity
y = k x
Total = (unit rate) (quantity)
To find unit rate:
K = 𝑦 𝑥
$ = (unit rate) (6)
$2.52 ÷ 6 = 0.42
Answer: A
p = n

16. Remember: Total = (constant of proportionality) (quantity)
Determine what is given and what still needs to be found and how it all fits into the equation 𝑦 = 𝑘𝑥.
Remember: Total = (constant of proportionality) (quantity) y = k x
Constant of proportionality
Total
Quantity
y = k x
Total = (constant of proportionality) (quantity)
c = p
Answer: A

17. Remember: Total = (constant of proportionality) (quantity)
Determine what is given and what still needs to be found and how it all fits into the equation 𝑦 = 𝑘𝑥.
Remember: Total = (constant of proportionality) (quantity) y = k x OR
Total
Quantity
Total
Quantity
y = k x
Total = (unit rate) (quantity)
To find unit rate:
K = 𝑦 𝑥
225 = (unit rate) (4.5)
225 ÷ 4.5 = 50
Answer: B
d = t
y = k x
Total = (unit rate) (quantity)
To find unit rate:
K = 𝑦 𝑥
375 = (unit rate) (7.5)
375 ÷ 7.5 = 50
d = t

18. Remember: Total = (constant of proportionality) (quantity)
7) You Try!
Determine what is given and what still needs to be found and how it all fits into the equation 𝑦 = 𝑘𝑥.
Remember: Total = (constant of proportionality) (quantity) y x k =
Answer: D

19. Remember: Total = (unit rate) (quantity)
8) You Try!
Determine what is given and what still needs to be found and how it all fits into the equation 𝑦 = 𝑘𝑥.
Remember: Total = (unit rate) (quantity) y x k =
Answer: C

20. Remember: Total = (constant of proportionality) (quantity)
9) You Try!
Determine what is given and what still needs to be found and how it all fits into the equation 𝑦 = 𝑘𝑥.
Remember: Total = (constant of proportionality) (quantity) y x k =
Answer: A

21. Remember: Total = (unit rate) (quantity)
10) You Try!
Determine what is given and what still needs to be found and how it all fits into the equation 𝑦 = 𝑘𝑥.
Remember: Total = (unit rate) (quantity) y x k =
Answer: B

22. End of PowerPoint