Intercept Definition

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The point of intersection of a curve of a function and the axes is known as its intercept. The intercept can be either x – intercept or y – intercept.

X – intercept is the point where the curve intersects the x – axis.

Y – intercept is the point where the curve intersects the y – axis.

Example 1: Given below is the graph of the function  y = 2x + 4. Find the intercepts of the function.





Solution:
The curve of the given function y = 2x + 4 is a straight line.

The straight line intersects both the axes at two distinct points. The curve of the function intersects the x – axis at x = - 2.

So the x – intercept of the given function is the point (- 2, 0).

At y = 4, the line intersects the y – axis . Thus the y – intercept of the given function is (0, 4).

Hence the intercepts of the given function are (-2,0) and (0,4).


Example 2: Find the intercepts of the following function y = -3x – 6. 





Solution:
As we can see in the graph, the curve of the given function is a straight line.

The line intersects the y – axis at -6. Thus the point of intersection of the curve and the y – axis is (0, -6).

The curve intersects the x – axis at x = - 2. Therefore the point of intersection of the x – axis and the curve is (- 2, 0)

Hence the intercepts of the given function are (-2, 0 ) and (0, -6).



 

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