Algebra

Lesson

In Sub In, we learnt how to substitute number values into equations to find a final value. Now we're going to use the same process and substitute one value into an equation to find the other unknown.

For example, if we were given the equation $y=2x$`y`=2`x` and asked to find the value of $y$`y` when $x=8$`x`=8, we would substitute in $8$8 for $x$`x` into the equation to work out that $y=2\times8$`y`=2×8$=$=$16$16.

A table of values is a nice, easy way to display this relationship between $x$`x` and $y$`y` values. Later on, we will use the $x$`x` and $y$`y` values as sets of coordinates to plot on a number line. But let's start by working through some examples and learn how to complete a table of values. Let's use the same equation as before, $y=2x$`y`=2`x`, to complete the following table.

$x$x |
$-1$−1 | $0$0 | $1$1 | $2$2 |
---|---|---|---|---|

$y$y |

We can substitute each of these $x$`x` values into the equation.

$2\times\left(-1\right)=-2$2×(−1)=−2

$2\times0=0$2×0=0

$2\times1=2$2×1=2 and $2\times2=4$2×2=4.

Let's write in these values to complete the table.

$x$x |
$-1$−1 | $0$0 | $1$1 | $2$2 |

$y$y |
$-2$−2 | $0$0 | $2$2 | $4$4 |

Do you notice how as the $x$`x` values increase by one, the $y$`y` values increase by two? Think about the rule and why this is the case.

Complete the table of values using the formula $t=-5s$`t`=−5`s`.

$s$ `s`$0$0 $1$1 $2$2 $3$3 $4$4 $t$ `t`$\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

Complete the table of values using the formula $q=2p-3$`q`=2`p`−3.

$p$ `p`$0$0 $1$1 $2$2 $3$3 $4$4 $q$ `q`$\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

Complete the table of values using the formula $q=-2p-3$`q`=−2`p`−3.

$p$ `p`$0$0 $1$1 $2$2 $3$3 $4$4 $q$ `q`$\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

Generalise the properties of operations with fractional numbers and integers.