Patterns · Second Year
Patterns
Second Year · Real-life linear patterns · Tap NEXT to begin
Section 1 of 2
A Real-Life Pattern
A pattern that grows by the same amount each step is linear. Its rule is $f(x) = mx + c$.
Worked example — the plumber’s fee
A plumber charges a €$50$ call-out fee plus €$30$ per hour. Make a table and find the rule $f(x)$ for the fee after $x$ hours.
Fees: $0\text{h}\!\to\!50,\ 1\!\to\!80,\ 2\!\to\!110,\ 3\!\to\!140$ — up $30$ each hour
Difference $m = 30$; start value $c = 50$
$f(x) = 30x + 50$
Section 2 of 2
Using the Rule
Now you try
You try
Using $f(x) = 30x + 50$, find the fee for a $5$-hour job.
Pen and paper out — try it before you reveal.
$f(5) = 30(5) + 50 = 150 + 50$
€$200$
€$200$
That’s Patterns.
Spot the constant difference, write $f(x)=mx+c$, and use it for any value.