Systems Of Linear Equations Word Problems: Graphing Worksheet - Free Printable

Let's solve this Graphing Linear Equations Vocabulary Worksheet step by step.

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Part 1: Fill in the blank spaces using the vocabulary list

We are given a coordinate plane diagram with labeled boxes pointing to different parts. We need to fill in each box with the correct term from the vocabulary list, without repeating any word.

#### Vocabulary List:
- Diagonal line
- Coordinate plane
- Quadrant 1
- Quadrant 2
- Quadrant 3
- Quadrant 4
- x-axis
- y-axis
- Horizontal line
- Vertical line
- x-intercept
- y-intercept
- Point
- Origin

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Now let’s analyze the diagram:

1. Top center (long horizontal rectangle) → This is the entire grid, so it should be:
✔ Coordinate plane

2. Horizontal line through the middle (x-axis) → The horizontal axis is called:
✔ x-axis

3. Vertical line through the middle (y-axis) → The vertical axis is called:
✔ y-axis

4. Where x-axis and y-axis intersect → This point is the:
✔ Origin

5. The diagonal line going from bottom-left to top-right → This is a:
✔ Diagonal line

6. Point where the diagonal line crosses the x-axis → This is the:
✔ x-intercept

7. Point where the diagonal line crosses the y-axis → This is the:
✔ y-intercept

8. Box pointing to a single dot on the line → This represents a:
✔ Point

9. The four regions divided by axes → These are the quadrants:
- Top right → Quadrant 1
- Top left → Quadrant 2
- Bottom left → Quadrant 3
- Bottom right → Quadrant 4

So assign accordingly:
- Upper right → Quadrant 1
- Upper left → Quadrant 2
- Lower left → Quadrant 3
- Lower right → Quadrant 4

10. A horizontal line (parallel to x-axis) → This is a:
✔ Horizontal line

11. A vertical line (parallel to y-axis) → This is a:
✔ Vertical line

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Now, based on typical labeling in such diagrams, here's how the blanks likely map:

| Box Location | Term |
|--------------|------|
| Top center (entire graph) | Coordinate plane |
| Horizontal axis | x-axis |
| Vertical axis | y-axis |
| Intersection of axes | Origin |
| Diagonal line | Diagonal line |
| Where diagonal crosses x-axis | x-intercept |
| Where diagonal crosses y-axis | y-intercept |
| A dot on the line | Point |
| Top-right quadrant | Quadrant 1 |
| Top-left quadrant | Quadrant 2 |
| Bottom-left quadrant | Quadrant 3 |
| Bottom-right quadrant | Quadrant 4 |
| Horizontal line (example) | Horizontal line |
| Vertical line (example) | Vertical line |

> ✔ All words used once — no repeats.

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Part 2: Plot the following points

We are given two sets of points to plot on separate grids.

#### a) Points:
(1,2), (4,2), (1,-1), (-1,2), (-2,-1), (2,0), (3,-3), (2,5)

How to plot:
- First number = x-coordinate (left/right)
- Second number = y-coordinate (up/down)

Let’s sketch them mentally or on paper:

- (1,2): Right 1, up 2
- (4,2): Right 4, up 2
- (1,-1): Right 1, down 1
- (-1,2): Left 1, up 2
- (-2,-1): Left 2, down 1
- (2,0): Right 2, on x-axis
- (3,-3): Right 3, down 3
- (2,5): Right 2, up 5

Plot all these on the first grid.

#### b) Points:
(-2,3), (1,3), (1,0), (-3,-1), (1,-4), (-5,0), (0,-6), (6,4)

- (-2,3): Left 2, up 3
- (1,3): Right 1, up 3
- (1,0): Right 1, on x-axis
- (-3,-1): Left 3, down 1
- (1,-4): Right 1, down 4
- (-5,0): Left 5, on x-axis
- (0,-6): On y-axis, down 6
- (6,4): Right 6, up 4

Plot these on the second grid.

> ✔ Just mark each point accurately on the graph paper.

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Part 3: Fill in the blanks

> "The co-ordinate plane is formed by a horizontal line, called ________, and a vertical line, called ________. The point where the x-axis crosses the y-axis is called the ________. Its coordinates are ________. The ________ gives the location on the x-axis and the ________ gives the location on the y-axis."

Let’s go step by step:

1. Horizontal line → x-axis
2. Vertical line → y-axis
3. Intersection point → Origin
4. Coordinates of origin → (0,0)
5. First number in a point → x-coordinate
6. Second number → y-coordinate

But wait — “x-coordinate” and “y-coordinate” are not in the original vocabulary list.

Looking back at the vocabulary list:
- We have: x-axis, y-axis, x-intercept, y-intercept, etc.
- But no "x-coordinate" or "y-coordinate" listed.

So we must use only words from the provided list.

But that seems problematic.

Wait — perhaps they expect us to use x-axis and y-axis again?

But that would repeat.

Alternatively, maybe the intended answer uses:

- The x-axis gives the location on the x-axis → but that doesn’t make sense.

Actually, the sentence says:
> "The ________ gives the location on the x-axis and the ________ gives the location on the y-axis."

This refers to the coordinates, not the axes.

But since "x-coordinate" and "y-coordinate" aren't in the list, perhaps the question allows x-axis and y-axis as placeholders? That wouldn’t be accurate.

Wait — recheck the vocabulary list:

It includes:
- x-axis
- y-axis
- x-intercept
- y-intercept
- Point
- Origin
- etc.

But no coordinate terms.

Hmm.

But the sentence is asking for what gives the location on each axis.

The first number in an ordered pair is the x-coordinate, which tells you where on the x-axis.

But since “x-coordinate” isn’t in the list, maybe the intended answer is:

> The x-axis gives the location on the x-axis...

No — that’s circular.

Alternatively, perhaps the worksheet expects:

> The x-intercept gives the location on the x-axis...

But that’s not true — the x-intercept is where a line crosses the x-axis, not a general location.

Wait — maybe it's a mistake.

But looking at similar worksheets, often the sentence is:

> The x-coordinate gives the location on the x-axis...

But since that’s not in the list, perhaps the intended answer is simply:

> The x-axis and y-axis — but that doesn't fit logically.

Wait — actually, re-read carefully:

> "The ________ gives the location on the x-axis and the ________ gives the location on the y-axis."

This is poorly worded if we're restricted to the list.

But note: the point has coordinates — but that’s not helpful.

Wait — maybe they mean:

> The x-intercept gives the location on the x-axis...?

No — only for lines.

But this is a general statement about the coordinate plane.

Given the constraints, perhaps the expected answers are:

- The x-axis gives the location on the x-axis → still awkward.

Alternatively, maybe the blank is meant for x-coordinate and y-coordinate, but since those aren’t in the list, perhaps the worksheet assumes we know them.

But the instruction says: "Fill in the blanks with appropriate words" — not necessarily from the list.

Wait — look back at the instructions:

> "Fill in the blanks with appropriate words"

But earlier, for part 1, it said: "using the list of words given alongside. You cannot repeat any word"

But part 3 does not say to use only the vocabulary list — so we can use standard math terms.

Therefore, even though they’re not in the list, we can use:

✔ x-coordinate and y-coordinate

So final answer:

> The co-ordinate plane is formed by a horizontal line, called x-axis, and a vertical line, called y-axis. The point where the x-axis crosses the y-axis is called the origin. Its coordinates are (0,0). The x-coordinate gives the location on the x-axis and the y-coordinate gives the location on the y-axis.

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✔ Final Answers:

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Part 1: Diagram Labels

| Box Position | Answer |
|-------------|--------|
| Top center | Coordinate plane |
| Horizontal axis | x-axis |
| Vertical axis | y-axis |
| Intersection | Origin |
| Diagonal line | Diagonal line |
| Crosses x-axis | x-intercept |
| Crosses y-axis | y-intercept |
| Dot on line | Point |
| Top-right quadrant | Quadrant 1 |
| Top-left quadrant | Quadrant 2 |
| Bottom-left quadrant | Quadrant 3 |
| Bottom-right quadrant | Quadrant 4 |
| Horizontal line example | Horizontal line |
| Vertical line example | Vertical line |

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Part 2: Plotting Points

- a) Plot: (1,2), (4,2), (1,-1), (-1,2), (-2,-1), (2,0), (3,-3), (2,5)
- b) Plot: (-2,3), (1,3), (1,0), (-3,-1), (1,-4), (-5,0), (0,-6), (6,4)

> Use graph paper to plot each point accurately.

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Part 3: Fill in the blanks

> The co-ordinate plane is formed by a horizontal line, called x-axis, and a vertical line, called y-axis. The point where the x-axis crosses the y-axis is called the origin. Its coordinates are (0,0). The x-coordinate gives the location on the x-axis and the y-coordinate gives the location on the y-axis.

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