Given:
The relation is
[tex]M = \{ (15k+9, 4), (3\cdot (4k-1), 6) \}[/tex]
To find:
The value of k for which the relation is not a function.
Solution:
A relation is a function if their exist a unique output or y value for each input or x values.
A relation is not a function if it has two y-values for single x value.
So, the given relation is not a function if x-coordinates of both ordered pairs are equal.
[tex]15k+9=3\cdot (4k-1)[/tex]
[tex]15k+9=12k-3[/tex]
Isolate variable terms.
[tex]15k-12k=-9-3[/tex]
[tex]3k=-12[/tex]
Divide both sides by 3.
[tex]k=-4[/tex]
Therefore, the given relation is not a function for k=-4.
