1. The problem asks us to find the form of any point on the line given by the equation $$y = 3x$$. 2. The equation $$y = 3x$$ means that for every value of $$x$$, the value of $$y$$ is three times $$x$$. 3. To express any point on this line, we can let $$x = a$$, where $$a$$ is any real number. 4. Substituting $$x = a$$ into the equation, we get $$y = 3a$$. 5. Therefore, any point on the line can be written as $$(a, 3a)$$. 6. Comparing this with the options given: - (a) $$(a, 3a)$$ matches our result. - (b) $$(3a, a)$$ does not satisfy $$y = 3x$$ because here $$y = a$$ and $$x = 3a$$, so $$y \neq 3x$$. - (c) $$(a, \frac{a}{3})$$ does not satisfy $$y = 3x$$ because here $$y = \frac{a}{3}$$ and $$x = a$$, so $$y \neq 3x$$. - (d) $$(\frac{a}{3}, -a)$$ does not satisfy $$y = 3x$$ because here $$y = -a$$ and $$x = \frac{a}{3}$$, so $$y \neq 3x$$. Final answer: (a) $$(a, 3a)$$