 Hong Kong
Stage 1 - Stage 3

# Substitution to Complete Table of Values

Lesson

Caption 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=2x 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=2x, 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.

#### Examples

##### question 1

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

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

##### question 2

Complete the table of values using the formula $q=2p-3$q=2p3.

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

##### question 3

Complete the table of values using the formula $q=-2p-3$q=2p3.

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