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.
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) |
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.
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) |
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 |
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) |
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.
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) |
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.
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) |
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 .