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.
Complete the table of values using the formula $t=-5s$t=−5s.
$s$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=2p−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=−2p−3.
$p$p | $0$0 | $1$1 | $2$2 | $3$3 | $4$4 |
---|---|---|---|---|---|
$q$q | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |