Year 7AC9M7A05

Tables of Values and Plotting Patterns

Generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane.

A rule, a table and a graph are three views of the same relationship. Being able to move between them is the whole skill.

Method

The rule tells you what to do to the input

y = 2x + 1

Put an $x$ in, get a $y$ out.

Build the table one column at a time

Substitute each $x$ value separately.

Points are written across then up

(3, 7)

The $x$ value always comes first.

e.g.

\text{Complete a table for } y = 2x + 1 \text{ and plot the points.}

Choose input values for $x$ . $x = 0,\ 1,\ 2,\ 3$
Substitute each one into the rule. $2(0)+1 = 1 \quad 2(1)+1 = 3$
Finish the table. $\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline y & 1 & 3 & 5 & 7 \end{array}$
Write each pair as a coordinate. $(0,1),\ (1,3),\ (2,5),\ (3,7)$
Plot them. They should lie in a straight line.
Describe the pattern in words. $\text{each time } x \text{ rises by } 1, \ y \text{ rises by } 2$

Build the table first, then read the pattern.

\text{Find } y \text{ when } x=5 \text{ for } y = 3x-2

Answer

13

\text{For } y = 4x, \text{ what happens to } y \text{ when } x \text{ rises by } 1?

Answer

y \text{ rises by } 4

\text{A table gives } (1,5),(2,8),(3,11). \text{ Find the rule.}

Answer

y = 3x + 2

\text{Plot } (2,-3). \text{ Which quadrant?}

Answer

\text{fourth}

\text{Why is } (3,7) \text{ not the same point as } (7,3)?

Answer

x \text{ is always written first.}