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Rules, tables and graphs: cheat sheet

Linear relations · The words and methods from the lessons, with an example of each.

growing pattern

What each new figure adds goes in front of nn; what is there at the start goes on its own. Figure 4 has 3×4+1=133 \times 4 + 1 = 13 sticks.

s=3n+1s = 3n + 1
Figure 4: each square adds 3 sticks, plus 1 at the start
Figure 4: each square adds 3 sticks, plus 1 at the start

ordered pair

Input first, then output. To plot it: across 2 on the xx-axis, then up 5.

(x,y)=(2,5)(x, y) = (2, 5)
The point (2, 5): across 2, up 5
The point (2, 5): across 2, up 5

rule

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

y=2x+1y = 2x + 1

table of values

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

x0123y1357\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 3 & 5 & 7 \end{array}

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.

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

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