---
title: "Rules, tables and graphs: cheat sheet"
subtitle: "Linear relations"
---

# Rules, tables and graphs

> The words and methods from this unit, with an example of each.

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**growing pattern**: What each new figure adds goes in front of $n$; what is there at the start goes on its own. Figure 4 has $3 \times 4 + 1 = 13$ sticks.

$$s = 3n + 1$$

_Figure 4: each square adds 3 sticks, plus 1 at the start_

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**rule**: A rule turns each input $x$ into an output $y$. Put the input in for $x$: $x = 3$ gives $y = 2 \times 3 + 1 = 7$.

$$y = 2x + 1$$

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**table of values**: Choose inputs, work out each output from the rule ($y = 2x + 1$ here), and write them in pairs.

$$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 3 & 5 & 7 \end{array}$$

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**ordered pair**: Input first, then output. To plot it: across 2 on the $x$-axis, then up 5.

$$(x, y) = (2, 5)$$

_The point (2, 5): across 2, up 5_

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**reading a graph**: Find the value you know on its axis, go to the line, then read across to the other axis. Sections of a graph increase, decrease or stay constant.

$$\text{axis} \to \text{line} \to \text{other axis}$$

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**vary one variable**: To see what one letter does, change only that letter and keep the others the same. Record the results in a table.

$$V = l \times w \times h \quad (\text{change } h \text{ only})$$

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