An equation of the type \(y=kx\ (k\ne 0)\) represents a line :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → passing through the origin
A point lies on a line when its coordinates satisfy the equation of the line. Putting \(x=0\) in \(y=kx\) gives \(y=k\times0=0\), so the origin \((0,0)\) lies on every such line, whatever the value of \(k\). The number \(k\) is the slope; it only decides how steeply the line rises or falls.
Why the other options are incorrect
Option (2) intersecting the coordinate axes at two different points — Incorrect. The line meets both axes only at the origin, which is one point, not two.
Option (3) parallel to x-axis — Incorrect. A line parallel to the x-axis has the form \(y=c\), with slope 0; here \(k\ne0\).
Option (4) parallel to y-axis — Incorrect. A line parallel to the y-axis has the form \(x=c\) and cannot be written in the form \(y=kx\).