Let’s solve this step by step.
We are given two function rules and tables to complete, then plot the points on coordinate planes, and finally compare them.
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First Rule: y = x + 3
We plug in each x-value into the rule to find y.
- When x = 1 → y = 1 + 3 =
4 → Ordered Pair: (1, 4)
- When x = 2 → y = 2 + 3 =
5 → Ordered Pair: (2, 5)
- When x = 3 → y = 3 + 3 =
6 → Ordered Pair: (3, 6)
- When x = 4 → y = 4 + 3 =
7 → Ordered Pair: (4, 7)
- When x = 5 → y = 5 + 3 =
8 → Ordered Pair: (5, 8)
✔ Table for y = x + 3 is already filled correctly in the image. We just need to list the ordered pairs:
Ordered Pairs for y = x + 3:
(1, 4), (2, 5), (3, 6), (4, 7), (5, 8)
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Second Rule: y = 3x
Again, plug in each x-value:
- When x = 1 → y = 3 × 1 =
3 → Ordered Pair: (1, 3)
- When x = 2 → y = 3 × 2 =
6 → Ordered Pair: (2, 6)
- When x = 3 → y = 3 × 3 =
9 → Ordered Pair: (3, 9)
- When x = 4 → y = 3 × 4 =
12 → Ordered Pair: (4, 12)
- When x = 5 → y = 3 × 5 =
15 → Ordered Pair: (5, 15)
✔ Table for y = 3x is also already filled correctly.
Ordered Pairs for y = 3x:
(1, 3), (2, 6), (3, 9), (4, 12), (5, 15)
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Now, plotting these on the coordinate plane:
For
y = x + 3, you’ll see a straight line going up slowly — it increases by 1 in y for every 1 increase in x. This is called a slope of 1.
For
y = 3x, you’ll see a steeper straight line — it increases by 3 in y for every 1 increase in x. Slope of 3.
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Compare the two graphs:
What differences do you notice?
→ The graph of
y = 3x rises much faster than
y = x + 3.
→ At x=1, y=3 vs y=4 → so at first, y=x+3 is higher.
→ But at x=2, y=6 vs y=5 → now y=3x is higher.
→ After x=1.5, y=3x stays above y=x+3 forever.
→ Also, y=3x goes through the origin (0,0), but y=x+3 does not — it crosses the y-axis at (0,3).
So main difference:
The rate of change (slope) is different — one grows faster than the other.
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Final Answer:
Ordered Pairs for y = x + 3:
(1, 4), (2, 5), (3, 6), (4, 7), (5, 8)
Ordered Pairs for y = 3x:
(1, 3), (2, 6), (3, 9), (4, 12), (5, 15)
Comparison:
The graph of y = 3x increases faster than y = x + 3. For small x-values (like x=1), y = x + 3 gives a larger y-value, but after x=1.5, y = 3x becomes larger and keeps growing faster. Also, y = 3x passes through (0,0), while y = x + 3 starts at (0,3).
Parent Tip: Review the logic above to help your child master the concept of ordered pairs worksheet.
