Tables, formulae and equations


The following example shows the same relationship represented in a table and as an equation for solving the missing variables.


Worked examples


Look at the table of values below: x


y


−2 −7


−1 −5


0 −3 1 −1


2 1


12 m


n 27


1 Describe the relationship between the y-values and the x-values in the table in the form: y = …


2 What is the value of m? 3 What is the value of n? 4 What do you notice about the y-values in the table? Is it possible to find an x-value for which the corresponding y-value is an even number?


Solutions


1 If x = −2, then y = −7, so: −7 = 2(−2) + c ∴ −7 = −4 + c ∴ c = −3 ∴ y = 2x − 3


2 y = 2(12) − 3 = 21, so m = 21


3 27 = 2x − 3 ∴ 2x = 30 ∴ x = 15, so n = 15


4 The y-values are all odd numbers. Let y = 2: 2 = 2x − 3 ∴ 2x = 5 ∴ x = 2,5. So for x = 2,5; y is an even number.


There is a constant difference of 2 between successive y-values. The equation for y will be of the form: y = 2x + c.


Substitute the value of x = 12 into the equation: y = 2x – 3.


Substitute the value of y = 27 into the equation: y = 2x – 3.


The y-values are all odd numbers. Choose any even value for y and solve for x.


Unit 4: Equivalent forms


133


CHAPTER 4


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