### Video Transcript

Use the rule to find the missing
number in this inputโoutput table. Rule equals three ๐ minus
seven.

We are told that when the input is
four, the output is five. To check this, we can substitute
the value ๐ equals four into the equation. Three ๐ means three times ๐, so
we are left with three multiplied by four minus seven. Three multiplied by four is 12. And taking away seven does give us
five. Our second set of values are an
input of five and an output of eight. Substituting five into the rule
does give us eight, as three multiplied by five is 15 and subtracting seven from
this is eight. We can do the same for an input of
seven, giving us an output of 14.

We need to calculate the missing
value in the table. This is the output when the input
is six. We can calculate the output by
substituting ๐ equals six into our rule. Three multiplied by six is equal to
18. Subtracting seven from this gives
us an answer of 11. When our input is six, our output
is 11.

An alternative method to solve this
question would be to notice that our rule, three ๐ minus seven, is a linear
function. This means that for every increase
of one to the input, the output will increase or decrease by the same value. This value is the coefficient of
๐, the number weโre multiplying by ๐, as this would be the slope or gradient of
the linear function. We can see this in our function
table as five plus three is equal to eight, eight plus three equals 11, and 11 plus
three is 14. As the input increases by one, the
corresponding output increases by three.