Intercept Definition
Intercept is come across in coordinate geometry.
Intercept is of two types. They are
Below, Intercept Definition for both types are given:
x intercept definition:
it is the x coordinate in the point on the x axis through which a straight line passes.
In the figure above, straight L passes through two points.
One A(a, 0) on x axis and another, B(0, b) on y axis.
According to intercept definition, the x coordinate in the point A (a, 0) is x intercept for the line L and the y coordinate b in the point B (0, b) is the y intercept for the line L.
Note:
For the x coordinate in A(a, 0) to become x intercept for line L, the straight line L must pass through the point A(a, 0) on x axis.
If the line L does not pass through this point A(a, 0), then a is not said to be any x intercept for the line L.
Similarly, for the y coordinate in B (0, b) to be called the y intercept of the line L, the straight line L must pass through this point lying on the y axis.
If the line L does not pass through this point B(0, b), then b is not said to be any y intercept for the line L.
In the above figure, let the point (a, 0) be (3, 0) and the point (0, b) be (0, 3). Then, a = 3 and b = 4.
So, the x intercept of the line L is 3, and the y intercept of the line is 4.
Interpretation of intercepts in terms of distance:
Aside from the above intercept definition, according to which intercepts are the respective coordinates, there is another way of understanding the intercepts of straight line L.
In the figure above, x intercept of the line L is (a, 0).
Therefore, x intercept denotes the distance from the origin on the x axis at which a line intersects the x axis.
Similarly, the distance from the origin on the y axis at which a line passes through the y axis is the y intercept.
How to find x intercept and y intercept of a straight line L
Using the intercept definition, the x intercept and y intercept of a straight line L can be found, provided the equation of the straight line L is given.
Question:
Find the x intercept and y intercept of the straight line L whose equation is
2x + 3y = 6
Solution:
From x intercept definition, x intercept is the x coordinate in the point (a, 0) through which the straight line L passes.
Now since the straight line L whose equation is 2x + 3y = 6 is passing through the point (a, 0), the x coordinate and y coordinate of the point (a, 0) can be substituted in the equation 2x + 3y = 6 of the given line L.
So, to find x intercept, of the straight line L whose equation is 2x + 3y = 6, substitute a in x and o in y, i.e.
2 (a) + 3(0) = 6, i.e 2a = 6, so a = 3.
Therefore, x intercept of the straight line l having equation 2x + 3y = 6 is 3.
Similarly, y intercept can be found.
According to y intercept definition, the straight line L must pass through the point B (0, b).
Therefore, the coordinates of the point B (0, b) can be substituted in the equation of the line L, i.e. 2x + 3y = 6
So, 2(0) + 3(b) = 6, i.e. 3b = 6, so b = 2.
Thus for the straight line L having equation 2x + 3y = 6, the
x intercept is 3, and the y intercept is 2.
YOU TRY:
What are the x intercept and y intercept of the straight line L whose equation is 4x + 9y = 36 using the intercept definition?
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