4 Free Spring Graphing Math Worksheets - Our Family Code - Free Printable

The image you've shared is a coordinate graphing activity titled *"Graphing Spring"*, where the goal is to plot and connect given coordinate pairs on a grid to reveal a hidden spring-themed image.

Let’s analyze and solve this step-by-step.

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🔍 Objective

Plot the given line segments (pairs of coordinates) on the coordinate plane, connecting each pair in order. The resulting shape will form a picture related to spring.

We are given several pairs of points:

```
(9,0)(9,5)
(9,5)(7,8)
(7,8)(5,9)
(5,9)(2,9)
(2,9)(3,6)
(3,6)(5,5)
(5,5)(9,5)
(9,5)(9,11)
(9,11)(10,12)
(10,12)(12,13)
(12,13)(13,15)
(13,15)(13,20)
(13,20)(12,18)
(12,18)(11,20)
(11,20)(9,20)
(9,20)(7,20)
(7,20)(6,18)
(6,18)(5,20)
(5,20)(5,15)
(5,15)(6,13)
(6,13)(8,12)
(8,12)(9,11)
```

We need to plot these points and connect them in order.

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🧩 Step-by-Step Solution

Let’s break down what happens when we connect these points.

#### 1. Start from (9,0) → (9,5)
This is a vertical line up from the bottom at x=9.

#### 2. (9,5) → (7,8)
Diagonal up-left.

#### 3. (7,8) → (5,9)
Continue up-left.

#### 4. (5,9) → (2,9)
Horizontal left.

#### 5. (2,9) → (3,6)
Down-right.

#### 6. (3,6) → (5,5)
Down-right.

#### 7. (5,5) → (9,5)
Horizontal right — this closes the lower part of a shape.

Now we have a closed loop from (9,0) to (9,5), then forming a kind of "stem" or base.

But wait — let's look at the next segment:
(9,5) → (9,11) — vertical up.

Then:
- (9,11) → (10,12)
- (10,12) → (12,13)
- (12,13) → (13,15)
- (13,15) → (13,20)
- (13,20) → (12,18)
- (12,18) → (11,20)
- (11,20) → (9,20)
- (9,20) → (7,20)
- (7,20) → (6,18)
- (6,18) → (5,20)
- (5,20) → (5,15)
- (5,15) → (6,13)
- (6,13) → (8,12)
- (8,12) → (9,11)

Wait — notice that (9,11) appears again at the end.

So we’re forming a symmetrical leaf-like shape, with a stem and two lobes.

Let’s now interpret the full structure.

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🌿 What Image Is This?

Looking at the plotted points and the already drawn lines in the image (which show a leaf), we can see:

- There is a stem going from (9,0) up to (9,5), then branching into a leaf.
- The top of the leaf has a pointed tip at (9,20).
- The leaf has two symmetrical sides, forming a broad leaf shape.
- The bottom left section looks like a smaller leaf or bud.

But here’s the key: the image already shows most of the leaf drawn, so the task is likely to complete it using the remaining lines.

Wait — actually, looking at the image, the leaf is already partially drawn. But the instruction says: *“Graph the lines below to reveal the Spring image.”*

So perhaps the lines listed are additional ones to draw to complete the image.

But let’s check: the current drawing already includes:

- A large leaf shape centered around x=9–13, y=14–21
- A stem from (9,0) to (9,5)
- A small shape near (4,5) to (8,9) — possibly a flower or bud

But the list of coordinates seems to describe the entire path, including the stem and leaf.

Let’s trace all the points together.

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✔ Let’s Plot All the Lines in Order

We’ll go through the list and see what shape forms.

1. (9,0) → (9,5) — Vertical stem up.
2. (9,5) → (7,8) — Diagonal up-left.
3. (7,8) → (5,9) — Up-left.
4. (5,9) → (2,9) — Left horizontal.
5. (2,9) → (3,6) — Down-right.
6. (3,6) → (5,5) — Right-down.
7. (5,5) → (9,5) — Right horizontal — this completes a lower petal or base.
- So far: a small closed shape at the bottom — maybe a bud or flower base.

Now continue:
8. (9,5) → (9,11) — Up along stem.
9. (9,11) → (10,12) — Up-right.
10. (10,12) → (12,13) — Up-right.
11. (12,13) → (13,15) — Up-right.
12. (13,15) → (13,20) — Up vertical.
13. (13,20) → (12,18) — Down-left.
14. (12,18) → (11,20) — Up-left.
15. (11,20) → (9,20) — Left horizontal.
16. (9,20) → (7,20) — Left.
17. (7,20) → (6,18) — Down-left.
18. (6,18) → (5,20) — Up-left.
19. (5,20) → (5,15) — Down vertical.
20. (5,15) → (6,13) — Down-right.
21. (6,13) → (8,12) — Right-down.
22. (8,12) → (9,11) — Right-down — connects back to earlier point.

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🎯 Final Shape Analysis

- From (9,0) to (9,5): Stem
- Then a small base/bud from (9,5) → (7,8) → (5,9) → (2,9) → (3,6) → (5,5) → (9,5) — forms a petal-like shape at the base.
- Then up the stem to (9,11), then forming a large leaf:
- From (9,11) to (13,20) — right side of leaf
- Then zig-zagging back: (13,20) → (12,18) → (11,20) → (9,20) → (7,20) → (6,18) → (5,20) → (5,15) → (6,13) → (8,12) → (9,11)
- This creates a symmetrical leaf with a central spine from (9,11) to (9,20), and lobes on both sides.

But wait — the image already shows a large leaf drawn from about (5,15) to (13,20), with a stem from (9,0) to (9,5), and a small shape on the left.

So the coordinates provided are meant to be plotted to complete the image.

But in fact, if you follow all the lines, you get:

- A stem from (9,0) to (9,5)
- A small flower or bud at the base
- A large leaf extending upward from (9,11) to (13,20) and back via (5,20), forming a symmetrical leaf

And finally, the top of the leaf is pointed at (9,20), which matches the current drawing.

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✔ Conclusion: The Image Is a Leaf

The completed shape is a leaf with:

- A stem at the bottom
- A small bud or base at the bottom
- A large, symmetrical leaf above

This is a classic spring symbol: a leaf sprouting, representing new growth.

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✔ Final Answer:

The image revealed by plotting the lines is a leaf, symbolizing spring growth.

To solve the problem:

1. Plot each coordinate pair on the grid.
2. Connect the dots in order as given.
3. The final shape is a leaf with a stem and a small bud, representing springtime renewal.

You’ve successfully revealed the Spring image — a leaf! 🌿

> 💡 Tip: Use a pencil and ruler to draw straight lines between each pair. You can color it in once complete!

Let me know if you'd like a visual sketch description or help tracing it!