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Additive Rules
Multiplicative Rules
Identify from the Table
Graph and Points
Mixed Practice
100

Write the rule (in the form y=x+a) for the relationship where (x) Kimora is 3 years older than Zane (y) . Then give the ordered pair when Zane is 12.

What is Rule: y=x+3

When Zane is 12: ordered pair (12,15)

100

Write the rule (in the form y=ax) for the relationship where each x is multiplied by 5 to get y. Give two ordered pairs for x = 1 and x = 3.

What is Rule: y=5x

Ordered pairs:

  • x=1 → (1,5)(1,5)
  • x=3 → (3,15)(3,15)
100

Given Table A (x: 2,6,9,12 → y: 4,8,11,14) and Table B (x: 2,5,8,11 → y: 4,10,16,22), which table is additive and which is multiplicative? (Answer with A or B and the rule.)

What is 

  • Table A: additive (y = x + 2). 
  • Table B: multiplicative (y = 2x). 
100

A graph shows points (1,4), (2,5), (3,6), (4,7). Is this additive or multiplicative? State the rule.

What is 

  • Points: (1,4), (2,5), (3,6), (4,7)
  • Differences in y: +1 for each +1 in x → additive with rule y=x+3 (check: 1+3=4; 2+3=5, etc.)
100

Write an ordered pair for third set of numbers in the table x->1,2,3,4 and y->3,4,5,6.

What is is at (3,5).

200

Using the rule y=x+6, complete the table for x = 3 and x = 5 and list the resulting ordered pairs.

What is y=x+6:

  • x = 3 → y=3+6=9→ (3,9)
  • x = 5 → y=5+6=11→ (5,11)
200

Complete the table for y=8x with x = 1, 3, 6, 10, and list the ordered pairs

What is 

  • For y=8x and x = 1, 3, 6, 10:
    • x=1 → y=8(1)=8 → (1,8)
    • x=3 → y=8(3)=24→ (3,24)
    • x=6 → y=8(6)=48 → (6,48)
    • x=10 → y=8(10)=80 → (10,80)
200

The table shows x: 2,5,8,11 and y: 22,55,88,121. Is this additive or multiplicative? Explain using a calculation

What is 

  • Table: x: 2,5,8,11 → y: 22,55,88,121
  • Check ratios: 22/2=11, 55/5=11, 88/8=11, 121/11=11 → multiplicative with factor 11: y=11x.
200

Which graph represents y=7x: (A) table with x: 0→8, y: 7→56 or (B) plotted points (2,14), (4,28), (6,42), (10,70)? Choose A, B, Both, or Neither and justify.

What is 

  • Which represents y=7x?
    • Table A (x,y): (0,7), (3,21), (5,35), (8,56) → note: if x=0, y should be 0 for y=7x, so Table A as printed with (0,7) is incorrect for y=7x.
    • Graph B shows points (2,14), (4,28), (6,42), (10,70), which are all multiples of 7 → Graph B correctly represents y = 7x for those x values.
    • Answer: B only.
200

Plot and label L:(7,0), M:(3,8), N:(4,1). Draw on whiteboard 

What is whiteboard answer 

300

Explain why the relationship in Noah’s table (x: 3, 8, 13, 18; y: 5, 10, 15, 20) is or is not represented by y=x+5

What is 

  • Noah’s table:
    • x: 3, 8, 13, 18
    • y: 5, 10, 15, 20 
    • If y=x+5, then for x = 3 → y = 8 (not 5). So the table is NOT y=x+5.
300

For y=0.2x, compute y when x = 5 and x = 9. Explain what kind of relationship this is and why

What is 

  • For y=0.2x:
    • x=5 → y=0.2(5)=1
    • x=9 → y=0.2(9)=1.8
300

The table shows x: 3,8,13,18 and y: 17,22,27,32. Identify the rule (write as y=x+a or y=ax) and justify.

What is 

  • Table: x: 3,8,13,18 → y: 17,22,27,32
  • Differences in y: +5 each time; differences in x: +5 each time 
  • Try form y=x+a: using x=3, y=17 → a = 14 → test: 8+14=22, 13+14=27, 18+14=32 → rule is y=x+14 (additive)
300

The graph plots points (1,6), (2,12), (3,18), (4,24). Identify the rule and explain whether the relationship is additive or multiplicative 

What is

  • Points (1,6), (2,12), (3,18), (4,24)
  • Multiplicative with the rule y=6x.
300

Marian’s pattern: each x-coordinate multiplied by 7 gives y-coordinate. List two ordered pairs from x = 2 and x = 4.

What is 

  • Marian: rule multiply x by 7 → pairs:
    • x=2 → (2,14)
    • x=4 → (4,28)
400

Create a table of four ordered pairs that represent the rule y=x+2.5, with x as 0,1,2,3. Then write the ordered pairs.

What is Table for y=x+2.5 with x = 0,1,2,3:

  • x=0 → y=0+2.5=2.5 → (0,2.5)
  • x=1 → y=1+2.5=3.5→ (1,3.5)
  • x=2 → y=2+2.5=4.5 → (2,4.5)
  • x=3 → y=3+2.5=5.5 → (3, 5.5)
400

Explain what makes y=5x different from y=x+3.

What is 

  • Difference between y=5x (multiplicative) and y=x+3 (additive)
400

Given the dog-park table (# of other dogs (x): 8,12,16,20 → total dogs(y): 11,15,19,23), decide additive or multiplicative and explain how to find the constant.

What is 

Dog-park table:

  • Other dogs: 8,12,16,20
  • Total dogs: 11,15,19,23
  • Differences in total dogs: +4 each time when other dogs increase by +4 → check y−x:
    • 11 − 8 = 3
    • 15 − 12 = 3
    • 19 − 16 = 3
    • 23 − 20 = 3
  • So rule: y=x+3 (additive). The constant is 3 (Henrietta's dogs)
400

Do the provided ordered pairs represents the rule y=x+4? (1,5), (2,6), (3,7), (4,8), (5,9), (6,10). Describe key features that confirm your choice. 

What is 

  • Rule y=x+4: graph with points (1,5), (2,6), (3,7), (4,8), (5,9), (6,10) (graph that shows y always 4 more than x). 
400

Dominic’s puppy: gained 3 pounds first week, then 2 pounds each subsequent week. Which graph (a–d) matches points (1,3), (2,5), (3,7), (4,9)? Is the relationship additive or multiplicative? Explain.

What is 

  • Dominic’s puppy: First-week gain 3 lb, then +2 lb each subsequent week → weights by week:
    • Week 1: 3
    • Week 2: 3 + 2 = 5
    • Week 3: 5 + 2 = 7
    • Week 4: 7 + 2 = 9
500

A scenario: The "feels like" temperature is 12 degrees more than the actual temperature. Write the rule and, for actual temperature x=95, compute y. Explain whether this is additive or multiplicative and why.

What is 

  • Rule: y=x+12
  • For x=95 → y=95+12=107
500

Mrs. Grant's cost rule: y=3.6x (y dollars for x photos). The provided table shows (2, 7.2), (3, 10.8), (5, 14.4), (8, 28.8). Determine if the table correctly represents the rule. If incorrect, explain. 

What is 

  • Mrs. Grant: rule y=3.6x
  • Provided table: (2, 7.2), (3, 10.8), (5, 14.4), (8, 28.8)
  • Check each:
    • x=2 → 3.6⋅2=7.2(correct)
    • x=3 → 3.6⋅3=10.8(correct)
    • x=5 → 3.6⋅5=18.0 (NOT 14.4) → provided table is incorrect at x=5
    • x=8 → 3.6⋅8=28.8 (correct)
  • Conclusion: The table is incorrect because the entry for x=5 should be 18.0, not 14.4.
500

Given a table of corresponding terms from two generated sequences (one sequence generated by "Add 3" starting at 0 and the other by "Add 6" starting at 0), describe your rule and table 

What is 

Example sequences:

  • Sequence A (Add 3 starting at 0): 0, 3, 6, 9, 12
  • Sequence B (Add 6 starting at 0): 0, 6, 12, 18, 24
  • Pair corresponding terms to make ordered pairs:
    • (0,0), (3,6), (6,12), (9,18), (12,24)
500

A graph has points (2,15), (3,20), (4,25), (6,35), (7,40). Choose the correct statement: (a) Additive; each y is 5 times x. (b) Additive; each y is 5 more than x. (c) Multiplicative; each y is higher than x. (d) Multiplicative; each y is 5 times x. (e) none of these are correct. Explain the correct answer.

What is 

  • None of these are correct
500

Using the rule y=x+6, complete the table for x = 3 and x = 5 and list the resulting ordered pairs. 

  • What is y=x+6:
    • x = 3 → y=3+6=9→ (3,9)
    • x = 5 → y=5+6=11→ (5,11)