# Difference between “intercept” and “intersect”

What is the difference between intercept and intersect? Can they be used interchangeably? For example, intersecting lines and intercepting lines.

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Intercept seems more appropriate as a noun (e.g. "Find the x-intercepts of f(x)"). Intersect seems more appropriate as a verb (e.g. "Find where f interests the x-axis") –  The Chaz 2.0 Oct 18 '12 at 5:45

The words "intercept" and "intersect" sound very similar but mean different things.

"Intersect" is a binary (two-valued) qualitative property of two or more sets and means that they have points in common, e.g., curves cross or areas overlap etc. Those points in common are called their "intersection." So, for example, every pair of sides of a triangle "intersect" at a point called the vertex of the triangle. In fact the word "vertex" REFERS to the point where two sides of a triangle meet. So as The Chaz commented, "intersect" is a verb.

On the other hand, an "intercept" is a quantitative property of of a curve. It refers to a specific point where the curve INTERSECTS one of the axes of the coordinate system, the particular axis lending its name to identify the intercept, such as "x intercept," etc. So an "intercept" is a particular intersection, usually referring to that point of a curve that is in common (crosses or first touches) another curve, usually a coordinate system axis.

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