Drawing Linear Graphs Textbook Exercise - Corbettmaths - Free Printable

You're working on Question 1, which asks you to:

> For each equation, complete the table of values and draw its graph for values of x from –1 to 3.

We’ll go through each part (a) to (d), fill in the missing y-values using the given equations, and then explain how to graph them.

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## ✔ PART (a): `y = 2x + 1`

We are given:
- x = -1 → y = -1 ✔
- x = 0 → y = 1 ✔
- x = 3 → y = 7 ✔

Now calculate missing values:

- x = 1:
y = 2(1) + 1 = 3

- x = 2:
y = 2(2) + 1 = 5

✔ Completed Table (a):

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

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## ✔ PART (b): `y = 3x - 1`

Given:
- x = -1 → y = -4 ✔
- x = 2 → y = 5 ✔

Calculate missing:

- x = 0:
y = 3(0) - 1 = -1

- x = 1:
y = 3(1) - 1 = 2

- x = 3:
y = 3(3) - 1 = 8

✔ Completed Table (b):

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

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## ✔ PART (c): `y = 2x - 3`

Given:
- x = 0 → y = -3 ✔
- x = 1 → y = -1 ✔

Calculate missing:

- 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 (c):

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

---

## ✔ PART (d): `y = x + 4`

This one has no values filled in — we need to 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 (d):

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

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## 📈 How to Graph Each Line

You have a coordinate grid with x from –1 to 3 and y from –2 to 8.

For each equation:

1. Plot the points from your completed table.
2. Connect the points with a straight line (since these are linear equations).
3. Extend the line slightly beyond the plotted points if needed to show the full trend.

Example: Graphing (a) `y = 2x + 1`

Points: (-1, -1), (0, 1), (1, 3), (2, 5), (3, 7)

Plot these 5 points → draw a straight line through them.

The line will slope upward (positive slope = 2), crossing the y-axis at (0,1).

Repeat this process for (b), (c), and (d).

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## 🔍 Key Observations

- All equations are linear → graphs are straight lines.
- The slope (coefficient of x) tells you how steep the line is.
- The constant term (like +1, -1, -3, +4) is the y-intercept — where the line crosses the y-axis (when x=0).

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## ✔ Final Answer Summary

(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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## 🖊️ Graphing Tip

Use different colors or labels for each line if drawing all on the same grid. You can also label each line with its equation.

Let me know if you’d like me to describe how to sketch the graphs step-by-step too!