X and Y Intercept
X and Yintercept are the lengths on the xaxis and yaxis, which is the distance of the point where the line or curve cuts the respective axis, from the origin. If the line cuts the xaxis at the point(a, 0), then 'a' is the xintercept, and if the line cuts the yaxis at the point (0, b), then 'b' is the yintercept. X and Yintercept are useful to find the slope, equation of a line, and also to find the area made by the line with the coordinate axes.
Let us learn more about how to find the x and yintercept, the graph, and the uses, with the help of examples, FAQs.
1.  What Are X And Y Intercept? 
2.  How To Find X And Y Intercept? 
3.  Graph Of X And Y Intercept 
4.  Uses Of X And Y Intercept 
5.  FAQs On X And Y Intercept 
What Are X And Y Intercept?
X and Yintercept is the distance on the axis from the origin where a line or a curve cuts the coordinate axis of the graph. When a line or curve cuts the xaxis at a point, the distance of this point from the origin is called xintercept and when that line or curve cuts the yaxis at a point, the distance of this point from the origin is called the yintercept.
X and y intercepts can be found from the points where the line or curve cuts the coordinate axis. If the line cuts the xaxis at the point (a, 0), then 'a' is the xintercept of the line, and if the line cuts the yaxis at the point (0,b), then 'b' is the yintercept of the line.
X intercept is the x value of the point where the line cuts the xaxis, and the Yintercept is the y value of the point where the line intersects the y axis. The x and yintercept is also called the horizontal intercept and vertical intercepts, since it is situated on the horizontal axis, and vertical axis respectively.
How To Find X And Y Intercept?
The x and yintercept can be easily found from the equations of a line. There are many forms of the equation of a line and the x and yintercept can be computed from the equations by substituting y = 0 and x = 0 in the equations respectively. Let us check some of the important equations of a line and how to find the x and yintercept respectively.
The slopeintercept form of the equation of a line is y = mx + c. Here x, y are the variables, m is the slope of the line and c is the yintercept. From this we can easily understand that the yintercept value is c, and the x intercept can be obtained by substituting y = 0 in this equation.
xintercept = c/m
yintercept = c
The general form of equation of a line is ax + by + c = 0. Here we substitute y = 0 in the equation and solve for x, to get the xintercept, and further substitute x = 0 in the same equation and solve for y, to get the yintercept of the line. Let us understand the calculations to find the x and y intercept, through the steps in the below table.
xintercept  yintercept 

Substitute y = 0 ax + b(0) + c = 0 ax + c = 0 x = c/a xintercept = c/a 
Substitute x = 0 a(0) + by + c = 0 by + c = 0 y = c/b yintercept = c/b 
Another important form of the equation of a line is the intercept form of the equation of a line and it is x/a + y/b = 1. From this equation itself, we can easily find the x and yintercept. Here from observing the equation, we can identify the xintercept as 'a' and the yintercept as 'b'. With this, we have understood the different methods to find the intercepts from the equations of a line.
Graph Of X And Y Intercept
X and yintercept can be found by observing the graph of the line. By knowing the points on the axis where the graph line cuts the coordinate axis, we can find the x and yintercept. Observe the below graph and try to find the points where the line cuts the xaxis and the yaxis.
Here, the xintercept is the distance from the origin on the xaxis and it is 4, as the line cuts the xaxis at the point (4,0). And the yintercept is the distance from the origin on the yaxis and it is 6 as the line cuts the yaxis at the point (0, 6).
Uses Of X And Y Intercept
The x and yintercept are useful to know the following aspects.
 The slope of the line can be calculated by dividing the yintercept by the xintercept of the line.
 The area of the triangle formed by the line with the two coordinate axes is equal to half of the product of the x and yintercepts.
 The x and yintercept are helpful to know the coordinates of the points where the line cuts the axis.
 The x and yintercept are useful to form the equation of a line, using the intercept form of the equation of a line.
 X and yintercept help us know the quadrant through which the line passes.
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Examples on X and Y Intercept

Example 1: Find x and y intercepts for the line 6x + 3y = 18.
Solution:
To find the xintercept substitute y = 0.
6x + 3(0) = 18
6x = 18
x = 18/6 = 3
The xintercept is 3 and the line cuts the xaxis at the point (3, 0).
Now to find the yintercept put x = 0.
6(0) + 3y = 18
3y = 18
y = 18/3
y = 6
The yintercept is 6, and the line cuts the yaxis at (6, 0).

Example 2: Draw the graph of 5x + 3y = 15 by finding the x and yintercepts.
Solution:
To find the x intercept substitute y = 0.
5x + 3(0) = 15
5x = 15
x = 15/5 = 3
The xintercept is 3, and the line cuts the xaxis at (3, 0).
To find the y intercept substitute x = 0 in the given equation.
5(0) + 3y = 15
3y = 15
y = 15/3 = 5
The yintercept is 5, and the line cuts the yaxis at (0, 5).
FAQs on X And Y Intercept
What Is X And Y Intercept In Coordinate Geometry?
The x and y intercept is the distance from the origin on the xaxis and yaxis where the line cuts the coordinate axis. If the line cuts the xaxis at the point (a, 0), then 'a' is the xintercept of the line, and if the line cuts the yaxis at the point (0, b) then 'b' is the yintercept of the line.
How To Find X And Y Intercept?
The x and yintercept can be easily calculated from the equation of a line. The substitution of x = 0 in the equation gives the yintercept and the substitution of y = 0 in the equation gives the xintercept.
What Is The X And Y Intercept In An Equation?
The x and y intercept in an equation of a line or a curve can be found by alternatively substituting x = 0 and y = 0 in the equation of the line. For a line having the equation ax + by + c = 0, the substitution of x = 0, and solving for y gives the y intercept as y = c/b, and substitution of y = 0 and solving for x gives the x intercept as x = c/a.
How to Find The X And Y Intercept For A Curve?
The x and yintercept for a curve can be found similar as we find for the line. The substitution of x = 0 in the equation of the curve and solving for the y value gives the yintercept, and by substituting y = 0 in the equation of the curve and solving for the x value gives the xintercept of the curve. The curve can have more than one x and yintercepts.
How To Find Slope From X And Y Intercept?
The slope of the line is the negative of the yintercept divided by the xintercept. The slope of a line with x and y intercept is yintercept/xintercept.
What Are The Instances Where There Are No X And Y Intercepts?
There are three instances when there is no x and yintercept for the line. If the line is parallel to the xaxis, if the line is parallel to the yaxis, and if the line is passing through the origin. The line drawn parallel to the xaxis has only the yintercept and does not have the xintercept. And the line drawn parallel to the y axis has only the xintercept and does not have the y intercept.
What Is The Use Of X And Y Intercept?
The x and y intercept is useful to find the slope of the line, to find the location of the line in the quadrants, and also to find the area of the triangle made by the line with the coordinate axis.
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