## 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. 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.
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) 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) Even line c is parallel to line a and line b .

Question 2.
Complete the table for the given rules. 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.
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) 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) 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. 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

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) 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. 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.
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) 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) All the 3 lines are parallel lines  and are shown in above graph .

Question 2.
Complete the table for the given rules. 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.
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) 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) All the 4 lines intersect at (0, 0 ) and is shown in the above graph .

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