9.7 Solving linear relations using multiple representations
Throughout this unit, we have seen there are many ways to work with a mathematical pattern, equation or function. The following example shows how each method can be used.
Worked example
Gemma buys a new phone on Sunday. She receives 32 GB of free data on her phone. From Monday, she uses 4 GB of data per day, every day. (i) Create a table to show how much data she has remaining after 5 days. (ii) Draw a graph to show this information. (iii) Find the slope (rate of change) of this graph. (iv) Explain this pattern in words, stating the amount of data remaining after any number of days.
(v) Write a mathematical formula to fi nd the amount of data Gemma has left on any particular day. Use your word sentence above to help.
(vi) Using either the table, graph or formula you have made, fi nd out how many days it will take for Gemma to use up all of her free data.
Solution (i)
By the end of this section you should be able to:
● solve a linear relation problem using a variety of ways
A pattern can be represented by an equation or function. Therefore, patterns, equations and functions are all interlinked.
(ii)
(iii)
You can choose diff erent values to fi nd the slope, and the answer should still be the same.