Eureka Math Grade 5 Module 6 Lesson 9 Answer Key

Engage NY Eureka Math 5th Grade Module 6 Lesson 9 Answer Key

Eureka Math Grade 5 Module 6 Lesson 9 Problem Set Answer Key

Question 1.
Complete the table for the given rules.
Engage NY Math Grade 5 Module 6 Lesson 9 Problem Set Answer Key 1
Line a
Rule: y is 1 more than x

x y

( x, y)

0
3
9
15

Line b
Rule: y is 4 more than x

x y

( x, y)

0
3
9
15

a. Construct each line on the coordinate plane above.
b. Compare and contrast these lines.
c. Based on the patterns you see, predict what line c, whose rule is y is 7 more than x, would look like. Draw your prediction on the plane above.
Answer:
a.
Line a
Rule: y is 1 more than x
y = x + 1

x y

( x, y)

0 1 (0, 1)
3 4 (3, 4)
9 10 (9, 10)
15 16 (15, 16)

Line b
Rule: y is 4 more than x
y = x + 4

x y

( x, y)

0 4 (0, 4)
3 7 (3, 7)
9 13 (9, 13)
15 19 (15, 19)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-9-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-9-Problem-Set-Answer-Key-Question-1
b. Lines a and b are parallel lines .
c. The line c
rule: y is 7 more than x
y = x + 7

x y

( x, y)

0 7 (0, 7)
3 10 (3, 10)
9 16 (9, 16)
15 22 (15, 22)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-9-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-9-Problem-Set-Answer-Key-Question-1-c
Even line c is parallel to line a and line b .

Question 2.
Complete the table for the given rules.
Engage NY Math Grade 5 Module 6 Lesson 9 Problem Set Answer Key 2
Line e
Rule: y is twice as much as x

x y

( x, y)

0
2
5
9

Line f
Rule: y is half as much as x

x y

( x, y)

0
6
10
20

a. Construct each line on the coordinate plane above.
b. Compare and contrast these lines.
c. Based on the patterns you see, predict what line g, whose rule is y is 4 times as much as x, would look like. Draw your prediction in the plane above.
Answer:
a.
Line e
Rule: y is twice as much as x
y = 2x

x y

( x, y)

0 0 (0, 0)
2 4 (2, 4)
5 10 (5, 10)
9 18 (9, 18)

Line f
Rule: y is half as much as x
y = x/2

x y

( x, y)

0 0 (0, 0)
6 3 (6, 3)
10 5 (10, 5)
20 10 (20, 10)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-9-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-9-Problem-Set-Answer-Key-Question-2
b. Both the lines e and f intersect at (0, 0)
c. line g
rule: y is 4 times as much as x
y = 4x

x y

( x, y)

0 0 (0, 0)
2 8 (2, 8)
5 20 (5, 20)
9 36 (9, 36)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-9-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-9-Problem-Set-Answer-Key-Question-2
All 3 lines intersect at (0, 0)

Eureka Math Grade 5 Module 6 Lesson 9 Exit Ticket Answer Key

Complete the table for the given rules. Then, construct lines l and m on the coordinate plane.
Eureka Math 5th Grade Module 6 Lesson 9 Exit Ticket Answer Key 1
Line l
Rule: y is 5 more than x

x y

( x, y)

0
1
2
4

Line m
Rule: y is 5 times as much as x

x y

( x, y)

0
1
2
4

Answer:
Line l
Rule: y is 5 more than x
y = x + 5

x y

( x, y)

0 5 (0, 5)
1 6 (1, 6)
2 7 (2, 7)
4 9 (4, 9)

Line m
Rule: y is 5 times as much as x
y = 5x

x y

( x, y)

0 0 (0, 0)
1 5 (1, 5)
2 10 (2, 10)
4 20 (4, 20)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-9-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-9-Exit-Ticket-Answer-Key-Question-1
Lines l and m are shown in the above graph .

Eureka Math Grade 5 Module 6 Lesson 9 Homework Answer Key

Question 1.
Complete the table for the given rules.
Eureka Math Grade 5 Module 6 Lesson 9 Homework Answer Key 1
Line a
Rule: y is 1 less than x

x y

( x, y)

1
4
9
16

Line b
Rule: y is 5 less than x

x y

( x, y)

5
8
14
20

a. Construct each line on the coordinate plane.
b. Compare and contrast these lines.
c. Based on the patterns you see, predict what line c, whose rule is y is 7 less than x, would look like. Draw your prediction on the plane above.
Answer:
a.
Line a
Rule: y is 1 less than x
y = x – 1

x y

( x, y)

1 0 (1, 0)
4 3 (4, 3)
9 8 (9, 8)
16 15 (16, 15)

Line b
Rule: y is 5 less than x
y = x – 5

x y

( x, y)

5 0 (5, 0)
8 3 (8, 3)
14 9 (14, 9)
20 15 (20, 15)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-9-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-9-Homework-Answer-Key-Question-1
b. Both the lines are a and b are parallel lines.
c.
Line c
Rule: y is 7 less than x
y = x – 7

x y

( x, y)

8 1 (8, 1)
14 7 (14, 7)
20 13 (20, 13)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-9-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-9-Homework-Answer-Key-Question-1-c
All the 3 lines are parallel lines  and are shown in above graph .

Question 2.
Complete the table for the given rules.
Eureka Math Grade 5 Module 6 Lesson 9 Homework Answer Key 2
Line e
Rule: y is 3 times as much as x

x y

( x, y)

0
1
4
6

Line f
Rule: y is a third as much as x

x y

( x, y)

0
3
9
15

a. Construct each line on the coordinate plane.
b. Compare and contrast these lines.
c. Based on the patterns you see, predict what line g, whose rule is y is 4 times as much as x, and line h, whose rule is y is one-fourth as much as x, would look like. Draw your prediction in the plane above.
Answer:
a.
Line e
Rule: y is 3 times as much as x
y = 3x

x y

( x, y)

0 0 (0, 0)
1 3 (1, 3)
4 12 (4, 12)
6 18 (6, 18)

Line f
Rule: y is a third as much as x

x y

( x, y)

0 0 (0, 0)
3 1 (3, 1)
9 3 (9, 3)
15 5 (15, 5)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-9-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-9-Homework-Answer-Key-Question-2
b. Both the lines e and f intersect at (0, 0)
c.
Line g
Rule: y is 4 times as much as x
y = 4x

x y

( x, y)

0 0 (0, 0)
3 12 (3, 12)
9 36 (9, 36)
15 60 (15, 60)

 

Line h
Rule: y is one-fourth as much as x
y = x/4

x y

( x, y)

0 0 (0, 0)
4 1 (4, 1)
8 2 (8, 2)
12 3 (12, 3)

Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-9-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-9-Homework-Answer-Key-Question-2-c
All the 4 lines intersect at (0, 0 ) and is shown in the above graph .

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