## Engage NY Eureka Math 5th Grade Module 6 Lesson 10 Answer Key

### Eureka Math Grade 5 Module 6 Lesson 10 Problem Set Answer Key

Question 1.

Use the coordinate plane below to complete the following tasks.

a. Line p represents the rule x and y are equal.

b. Construct a line, d, that is parallel to line p and contains point D.

c. Name 3 coordinate pairs on line d.

d. Identify a rule to describe line d.

e. Construct a line, e, that is parallel to line p and contains point E.

f. Name 3 points on line e.

g. Identify a rule to describe line e.

h. Compare and contrast lines d and e in terms of their relationship to line p.

Answer:

a. Yes, Line p represents the rule x and y are equal because all x and y coordinates are equal .

Some of the coordinate points on line p are ( 1, 1) , (2, 2) .

b. A line, d, that is parallel to line p and contains point D is shown in below graph with coordinate points (1, 3) and (3, 5)

c. The 3 coordinate pairs on line d are (1, 3) , (1\(\frac{1}{2}\), 3\(\frac{1}{2}\)) and (3\(\frac{1}{2}\), 5\(\frac{1}{2}\)) .

d. A rule for line d, is y is 2 more than x .

e. A line, e, that is parallel to line p and contains point E .

f . 3 points that are on line e are (2, 1) , ( 3, 2) and (5, 4).

g. A rule for line e, is y is 1 less than x .

h. Line p is parallel to line d and line p is parallel to line e .

Question 2.

Write a rule for a fourth line that would be parallel to those above and would contain the point (3\(\frac{1}{2}\), 6). Explain how you know.

Answer:

First plot the point F (3\(\frac{1}{2}\), 6) and draw a line that is parallel to line p , d and e.

Question 3.

Use the coordinate plane below to complete the following tasks.

a. Line p represents the rule x and y are equal.

b. Construct a line, v, that contains the origin and point V.

c. Name 3 points on line v.

d. Identify a rule to describe line v.

e. Construct a line, w, that contains the origin and point W.

f. Name 3 points on line w.

g. Identify a rule to describe line w.

h. Compare and contrast lines v and w in terms of their relationship to line p.

i. What patterns do you see in lines that are generated by multiplication rules?

Answer:

a. Yes , Line p represents the rule x and y are equal because the coordinates of x and y are equal .

two coordinate points on line p are (1, 1) and (8, 8)

b.

c. The 3 points on line v are ( 2, 4) , (3,6) and ( 4, 8).

d. The rule to describe line v is the y coordinate is double the x coordinate .

e.

f. The 3 points on line w are (2, 1), (4, 2) and ( 10, 5)

g. The rule to describe line w is the y coordinate is half of x coordinate .

h. The line v is steeper and line w is shallower than p . The rule used is multiplication of x but line v multiplies by a greater number .

i. They are not parallel lines because in line p the x and y coordinates are equal . The v and w lines are stepper and shallower respectively .

Question 4.

Circle the rules that generate lines that are parallel to each other.

add 5 to x

multiply x by \(\frac{2}{3}\)

x plus \(\frac{1}{2}\)

x times 1\(\frac{1}{2}\)

Answer:

### Eureka Math Grade 5 Module 6 Lesson 10 Exit Ticket Answer Key

Use the coordinate plane below to complete the following tasks.

a. Line p represents the rule x and y are equal.

b. Construct a line, a, that is parallel to line p and contains point A.

c. Name 3 points on line a.

d. Identify a rule to describe line a.

Answer:

b.

c. The 3 points on line a are (4, 1) , ( 5, 2) and (6, 3)

d. The rule to describe line a is the y coordinate is 3 less than x coordinate .

### Eureka Math Grade 5 Module 6 Lesson 10 Homework Answer Key

Question 1.

Use the coordinate plane to complete the following tasks.

a. Line p represents the rule x and y are equal.

b. Construct a line, d, that is parallel to line p and contains point D.

c. Name 3 coordinate pairs on line d.

d. Identify a rule to describe line d.

e. Construct a line, e, that is parallel to line p and contains point E.

f. Name 3 points on line e.

g. Identify a rule to describe line e.

h. Compare and contrast lines d and e in terms of their relationship to line p.

Answer:

b.

c. The 3 coordinates pairs of line d are (1, 3) , (2, 4) and (3, 5).

d. The rule to describe line d is the y coordinate is 2 more than the x coordinate .

e.

f. The 3 points on line e are (2, 1) , (3, 2) and (5, 4) .

g. The rule to describe line e is the y coordinate is 1 less than the x coordinate .

h. Line d and Line e are both parallel to line p .

Question 2.

Write a rule for a fourth line that would be parallel to those above and that would contain the point (5\(\frac{1}{2}\), 2). Explain how you know.

Answer:

Explanation :

First mark the point F ((5\(\frac{1}{2}\), 2)) and then draw a line that is parallel to line p .

The 3 coordinate points on line f are (4, \(\frac{1}{2}\)) , (4 \(\frac{1}{2}\), 1 ) and (6 , 2\(\frac{1}{2}\)).

The rule for line f is the y coordinate is 3\(\frac{1}{2}\) less than the x coordinate .

Question 3.

Use the coordinate plane below to complete the following tasks.

a. Line p represents the rule x and y are equal.

b. Construct a line, v, that contains the origin and point V.

c. Name 3 points on line v.

d. Identify a rule to describe line v.

e. Construct a line, w, that contains the origin and point W.

f. Name 3 points on line w.

g. Identify a rule to describe line w.

h. Compare and contrast lines v and w in terms of their relationship to line p.

i. What patterns do you see in lines that are generated by multiplication rules?

Answer:

b.

c. The 3 points on line v are (1, 2) , ( 2, 4) and (5, 10) .

d. The rule to describe the line v is the y coordinate is double the x coordinate .

e.

f. The 3 coordinate points on line w are ( 2, 1), (4, 2) and (6, 3) .

g. The rule to describe the line w is the y coordinate is half of x coordinate .

h. The line v is steeper and line w is shallower than p . The rule used is multiplication of x but line v multiplies by a greater number .

i. They are not parallel lines because in line p the x and y coordinates are equal . The v and w lines are stepper and shallower respectively .