We will discuss here about the intercepts made by a straight line on axes or intercepts of a line made on the axes of reference.
Let a straight line ‘MN’ does not passes through the origin which meets xaxis in the point M and yaxis in the point N, then the intercept made by the line MN on xaxis is OM i.e., OM is called xintercept.
Again, the intercept made by the line MN on yaxis is ON i.e., ON is called yintercept
Both OM and ON called the intercepts made by the line MN on both xaxis and yaxis.
The line intercept between the axes is the line MN.
Let AB be a line cutting the xaxis and the yaxis at A and B respectively on the positive sides of the axes. Let OA = a and OB = b. Then, the intercepts made on the axes of reference by the line are a and b respectively. So, xintercept = a, and yintercept = b.
Convention for the signs of intercepts:
The xintercept is considered positive if it is measured to the right of the origin
The yintercept is considered positive if it is measured above the origin
The xintercept is considered negative if measured to the left of the origin.
If A is on the negative side of the xaxis, the intercept on the xaxis (i.e., xintercept) is = a.
The yintercept is considered negative if measured below the origin.
If B is on the negative side of the yaxis, the intercept on the yaxis (i.e., yintercept) is = b.
Notes:
(i) When a straight line passes through origin then it makes zero intercepts on axis.
(ii) Any horizontal straight line has no xintercept
(iii) Any a vertical line has no yintercept.
(iii) The intercepts on xaxis is denoted by a
(iv) The intercepts on yaxis is denoted by b.
(v) When a straight line has only yintercept, then the intercept denoted by c.
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