Linear Functions worksheet for plotting and analyzing equations on a coordinate plane.

Let’s solve this step by step.

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Section A:

We are given 8 equations:
y = 3, x = 2, y = -3, x = 1, y = 6, x = 0, y = 0, x = -6

These are all horizontal or vertical lines.

- Horizontal lines (like y = 3) go left-right at that y-value.
- Vertical lines (like x = 2) go up-down at that x-value.

The table asks for the intersection points of specific pairs:

1. x = 2 and y = 3 → Where do these two lines meet? At point (2, 3)
2. x = 2 and y = -3 → Meet at (2, -3)
3. x = 1 and y = 6 → Meet at (1, 6)
4. x = -6 and y = 0 → Meet at (-6, 0)

All intersections are just the combination of the x and y values — since one is fixed x and the other fixed y, they cross exactly at (x, y).

✔ So coordinates are:
- (2, 3)
- (2, -3)
- (1, 6)
- (-6, 0)

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Section B:

Function: y = x

This means whatever x is, y is the same.

So fill in the table:

| 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) |

Then plot those points on the graph — they’ll form a straight diagonal line through the origin.

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Final Answer:

Section A – Coordinates of intersection:
(2, 3), (2, -3), (1, 6), (-6, 0)

Section B – Table filled as above; plotted points lie on the line y = x.