Final answer:
When x is tripled in the relation y=kx, y also triples, thus the correct option is a.
Step-by-step explanation:
In the given relation, y=kx, k is a constant that represents the slope or rate of change of the line. This means that for every increase of 1 unit in x, there will be a corresponding increase of k units in y.
Now, if we triple x, it means that x is increased by 3 units. Therefore, the corresponding increase in y will be 3k units. This shows that y also triples when x is tripled.
To understand this concept further, let us consider an example. Let k=2 and x=3. This means that y=2*3=6. Now, if we triple x, it becomes 9 and the corresponding increase in y will be 3*2=6. This shows that y also triples from 6 to 18 when x is tripled from 3 to 9.
In mathematical terms, we can represent this relationship as y=2x. When x is tripled, it becomes 3x. Therefore, the new equation will be y=2*3x=6x. This clearly shows that y has tripled from 2x to 6x when x is tripled.
In summary, when x is tripled in the relation y=kx, y also triples. This is because the constant k remains the same, and for every increase of 1 unit in x, there will be a corresponding increase of k units in y. Hence, when x is increased by 3 units, y will also increase by 3k units, which leads to a tripled value of y.