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:
| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | -1 | 1 | ? | ? | 7 |

Let’s calculate missing $ y $ values:

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

✔ Completed table:
| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | -1 | 1 | 3 | 5 | 7 |

Graphing:
Plot the points: $(-1, -1), (0, 1), (1, 3), (2, 5), (3, 7)$ and join them with a straight line.

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(b) $ y = 3x - 1 $

Given:
| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | -4 | ? | ? | 5 | ? |

Calculate missing values:

- $ 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 |

Graphing:
Plot: $(-1, -4), (0, -1), (1, 2), (2, 5), (3, 8)$ and draw a straight line through them.

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(c) $ y = 2x - 3 $

Given:
| $ x $ | -1 | 0 | 1 | 2 | 3 |
|--------|----|---|---|---|---|
| $ y $ | ? | -3 | -1 | ? | ? |

Calculate missing values:

- $ 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 |

Graphing:
Plot: $(-1, -5), (0, -3), (1, -1), (2, 1), (3, 3)$ and connect with a straight line.

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(d) $ y = x + 4 $

No values given — we need to compute all.

For $ x = -1 $ to $ x = 3 $:

- $ 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 |

Graphing:
Plot: $(-1, 3), (0, 4), (1, 5), (2, 6), (3, 7)$ and draw a straight line.

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✔ Summary of All Completed Tables:

(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

1. Use the coordinate grid provided.
2. For each equation, plot the five points from the table.
3. Join the points with a straight line (use a ruler).
4. The lines should extend slightly beyond the plotted points if possible.

> 💡 Tip: The general form is $ y = mx + c $.
> - $ m $ is the gradient (slope)
> - $ c $ is the y-intercept (where the line crosses the y-axis)

For example:
- (a) $ y = 2x + 1 $ → slope = 2, y-intercept = 1
- (b) $ y = 3x - 1 $ → slope = 3, y-intercept = -1
- (c) $ y = 2x - 3 $ → slope = 2, y-intercept = -3
- (d) $ y = x + 4 $ → slope = 1, y-intercept = 4

You can use these to check your graph: start at the y-intercept, then go up/down based on the slope.

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Let me know if you'd like a visual sketch or help plotting!