Drawing Linear Graphs Textbook Exercise - Corbettmaths - Free Printable

Let's solve Question 1 step by step. We are asked to:

1. Complete the table of values for each linear equation using $ x $ values from $-1$ to $3$.
2. Draw the graph of each equation (we’ll describe how to plot it, since we can’t draw here).

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(a) $ y = 2x + 1 $

We already have some values filled in:
- When $ x = -1 $: $ y = 2(-1) + 1 = -2 + 1 = -1 $ ✔
- When $ x = 0 $: $ y = 2(0) + 1 = 1 $ ✔
- When $ x = 3 $: $ y = 2(3) + 1 = 6 + 1 = 7 $ ✔

Now calculate missing ones:

- $ x = 1 $: $ y = 2(1) + 1 = 2 + 1 = 3 $
- $ x = 2 $: $ y = 2(2) + 1 = 4 + 1 = 5 $

✔ Completed table:

| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | -1 | 1 | 3 | 5 | 7 |

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(b) $ y = 3x - 1 $

Given:
- $ x = -1 $: $ y = 3(-1) - 1 = -3 - 1 = -4 $ ✔
- $ x = 2 $: $ y = 3(2) - 1 = 6 - 1 = 5 $ ✔

Now compute others:

- $ x = 0 $: $ y = 3(0) - 1 = -1 $
- $ x = 1 $: $ y = 3(1) - 1 = 3 - 1 = 2 $
- $ x = 3 $: $ y = 3(3) - 1 = 9 - 1 = 8 $

✔ Completed table:

| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | -4 | -1 | 2 | 5 | 8 |

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(c) $ y = 2x - 3 $

Given:
- $ x = 0 $: $ y = 2(0) - 3 = -3 $ ✔
- $ x = 1 $: $ y = 2(1) - 3 = 2 - 3 = -1 $ ✔

Now compute others:

- $ x = -1 $: $ y = 2(-1) - 3 = -2 - 3 = -5 $
- $ x = 2 $: $ y = 2(2) - 3 = 4 - 3 = 1 $
- $ x = 3 $: $ y = 2(3) - 3 = 6 - 3 = 3 $

✔ Completed table:

| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | -5 | -3 | -1 | 1 | 3 |

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(d) $ y = x + 4 $

No values given — let’s compute all:

- $ x = -1 $: $ y = -1 + 4 = 3 $
- $ x = 0 $: $ y = 0 + 4 = 4 $
- $ x = 1 $: $ y = 1 + 4 = 5 $
- $ x = 2 $: $ y = 2 + 4 = 6 $
- $ x = 3 $: $ y = 3 + 4 = 7 $

✔ Completed table:

| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | 3 | 4 | 5 | 6 | 7 |

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✔ Final Answers:

#### (a) $ y = 2x + 1 $
| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | -1 | 1 | 3 | 5 | 7 |

#### (b) $ y = 3x - 1 $
| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | -4 | -1 | 2 | 5 | 8 |

#### (c) $ y = 2x - 3 $
| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | -5 | -3 | -1 | 1 | 3 |

#### (d) $ y = x + 4 $
| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | 3 | 4 | 5 | 6 | 7 |

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📈 How to Draw the Graphs

For each equation:

1. Plot the points from the completed table on the grid.
2. Connect the points with a straight line (since these are linear equations).
3. The line should extend beyond the plotted points if possible.

> Example: For $ y = 2x + 1 $, plot points:
> (-1, -1), (0, 1), (1, 3), (2, 5), (3, 7) → then draw a straight line through them.

Each graph will be a straight line with different slopes and intercepts.

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🔍 Summary of Key Features

| Equation | Gradient (slope) | Y-intercept |
|----------------|------------------|-------------|
| $ y = 2x + 1 $ | 2 | 1 |
| $ y = 3x - 1 $ | 3 | -1 |
| $ y = 2x - 3 $ | 2 | -3 |
| $ y = x + 4 $ | 1 | 4 |

These help you sketch quickly: start at the y-intercept, then use the slope to go up/down and right/left.

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✔ You now have all tables completed and are ready to draw the graphs! Let me know if you'd like help plotting them or interpreting the graphs.