Question:
The equation of the line passing through the origin and having a slope of \(\frac{1}{\sqrt{3}}\) is
The equation of the line passing through the origin and having a slope of \(\frac{1}{\sqrt{3}}\) is
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For a line through the origin, simply use \(y=mx\). After substituting the slope, simplify the equation into the form given in the options.
Updated On: Jun 15, 2026
- \(y=\sqrt{3}x\)
- \(y=3x\)
- \(3y=x\)
- \(x=\sqrt{3}y\)
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The Correct Option is D
Solution and Explanation
Concept:
The equation of a straight line passing through the origin is
\[
y=mx,
\]
where \(m\) is the slope of the line.
Step 1: Substitute the given slope. Given \[ m=\frac{1}{\sqrt3}. \] Therefore, \[ y=\frac{x}{\sqrt3}. \]
Step 2: Remove the denominator. Multiplying both sides by \(\sqrt3\), \[ \sqrt3\,y=x. \] Hence, \[ x=\sqrt3\,y. \] This matches option (D).
Step 1: Substitute the given slope. Given \[ m=\frac{1}{\sqrt3}. \] Therefore, \[ y=\frac{x}{\sqrt3}. \]
Step 2: Remove the denominator. Multiplying both sides by \(\sqrt3\), \[ \sqrt3\,y=x. \] Hence, \[ x=\sqrt3\,y. \] This matches option (D).
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