Which one of the following options is true, and why?
For the equation \(y = 3x + 5\):
(i) a unique solution
(ii) only two solutions
(iii) infinitely many solutions
(iii), because for every value of x, there is a corresponding value of y and vice-versa.
The equation \(y = 3x + 5\) is a straight line. Any value of \(x\) produces exactly one value of \(y\), and every point on that line is a solution.
A line in the plane has infinitely many points, so the equation has infinitely many solutions. That matches option (iii).