KS3 and KS4 Linear Functions Worksheets - Graphing Linear ... - Free Printable

Let’s solve this step by step.

We are given several linear functions to plot and then find where they intersect — meaning, where two lines cross each other on the graph. The point where they cross is called the “point of intersection,” and we write it as (x, y).

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Section A: Plot and label the functions. Then state the coordinates of the intersections below.

We’re given these equations:

- y = 3 → horizontal line at y=3
- x = 2 → vertical line at x=2
- y = -3 → horizontal line at y=-3
- x = 1 → vertical line at x=1
- y = 6 → horizontal line at y=6
- x = 0 → vertical line at x=0 (this is the y-axis!)
- y = 0 → horizontal line at y=0 (this is the x-axis!)
- x = -6 → vertical line at x=-6

Now, let’s look at the table in Section A that asks for coordinates of intersection:

| x | y | Coordinates of intersection |
|-------|-------|-----------------------------|
| x = 2 | y = 3 | ? |
| x = 2 | y = -3| ? |
| x = 1 | y = 6 | ? |
| x = -6| y = 0 | ? |

To find the point where a vertical line (like x = 2) meets a horizontal line (like y = 3), you just combine them!

Why? Because:
- x = 2 means every point on that line has x-coordinate 2.
- y = 3 means every point on that line has y-coordinate 3.
→ So the only point that satisfies both is (2, 3)

Same logic applies to all:

1. x = 2 and y = 3 → Point is (2, 3)
2. x = 2 and y = -3 → Point is (2, -3)
3. x = 1 and y = 6 → Point is (1, 6)
4. x = -6 and y = 0 → Point is (-6, 0)

✔ These are straightforward because one equation gives you x, the other gives you y — so together they give you the full coordinate pair.

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Section B: Plot and label each function.

We’re given a table with values of x from -1 to 4, and we need to calculate y = x for each, then write the coordinates.

Remember: y = x means whatever x is, y is the same.

So:

- When x = -1 → y = -1 → Coordinate: (-1, -1)
- When x = 0 → y = 0 → Coordinate: (0, 0)
- When x = 1 → y = 1 → Coordinate: (1, 1)
- When x = 2 → y = 2 → Coordinate: (2, 2)
- When x = 3 → y = 3 → Coordinate: (3, 3)
- When x = 4 → y = 4 → Coordinate: (4, 4)

You would plot these points on the grid and draw a straight line through them — it will be a diagonal line going up to the right, passing through the origin.

But since the question doesn’t ask for anything else in Section B (no specific intersections or questions), we just fill in the table.

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Final Answer:

Section A – Coordinates of Intersection:

- x = 2, y = 3 → (2, 3)
- x = 2, y = -3 → (2, -3)
- x = 1, y = 6 → (1, 6)
- x = -6, y = 0 → (-6, 0)

Section B – Table Completion:

| x | y = x | Coordinates |
|----|--------|-------------|
| -1 | -1 | (-1, -1) |
| 0 | 0 | (0, 0) |
| 1 | 1 | (1, 1) |
| 2 | 2 | (2, 2) |
| 3 | 3 | (3, 3) |
| 4 | 4 | (4, 4) |