X and Y Intercept
X and Y-intercept are the lengths on the x-axis and y-axis, which is the distance of the point where the line or curve cuts the respective axis, from the origin. If the line cuts the x-axis at the point(a, 0), then 'a' is the x-intercept, and if the line cuts the y-axis at the point (0, b), then 'b' is the y-intercept. X and Y-intercept 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 y-intercept, 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 Y-intercept 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 x-axis at a point, the distance of this point from the origin is called x-intercept and when that line or curve cuts the y-axis at a point, the distance of this point from the origin is called the y-intercept.
X and y intercepts can be found from the points where the line or curve cuts the coordinate axis. If the line cuts the x-axis at the point (a, 0), then 'a' is the x-intercept of the line, and if the line cuts the y-axis at the point (0,b), then 'b' is the y-intercept of the line.
X intercept is the x value of the point where the line cuts the x-axis, and the Y-intercept is the y value of the point where the line intersects the y axis. The x and y-intercept 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 y-intercept can be easily found from the equations of a line. There are many forms of the equation of a line and the x and y-intercept 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 y-intercept respectively.
The slope-intercept 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 y-intercept. From this we can easily understand that the y-intercept value is c, and the x intercept can be obtained by substituting y = 0 in this equation.
x-intercept = -c/m
y-intercept = 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 x-intercept, and further substitute x = 0 in the same equation and solve for y, to get the y-intercept of the line. Let us understand the calculations to find the x and y intercept, through the steps in the below table.
| x-intercept | y-intercept |
|---|---|
|
Substitute y = 0 ax + b(0) + c = 0 ax + c = 0 x = -c/a x-intercept = -c/a |
Substitute x = 0 a(0) + by + c = 0 by + c = 0 y = -c/b y-intercept = -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 y-intercept. Here from observing the equation, we can identify the x-intercept as 'a' and the y-intercept 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 y-intercept 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 y-intercept. Observe the below graph and try to find the points where the line cuts the x-axis and the y-axis.
Here, the x-intercept is the distance from the origin on the x-axis and it is -4, as the line cuts the x-axis at the point (-4,0). And the y-intercept is the distance from the origin on the y-axis and it is 6 as the line cuts the y-axis at the point (0, 6).
Uses Of X And Y Intercept
The x and y-intercept are useful to know the following aspects.
- The slope of the line can be calculated by dividing the y-intercept by the x-intercept 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 y-intercepts.
- The x and y-intercept are helpful to know the coordinates of the points where the line cuts the axis.
- The x and y-intercept are useful to form the equation of a line, using the intercept form of the equation of a line.
- X and y-intercept help us know the quadrant through which the line passes.
☛ Related Topics
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 x-axis and y-axis where the line cuts the coordinate axis. If the line cuts the x-axis at the point (a, 0), then 'a' is the x-intercept of the line, and if the line cuts the y-axis at the point (0, b) then 'b' is the y-intercept of the line.
How To Find X And Y Intercept?
The x and y-intercept can be easily calculated from the equation of a line. The substitution of x = 0 in the equation gives the y-intercept and the substitution of y = 0 in the equation gives the x-intercept.
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 y-intercept 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 y-intercept, and by substituting y = 0 in the equation of the curve and solving for the x value gives the x-intercept of the curve. The curve can have more than one x and y-intercepts.
How To Find Slope From X And Y Intercept?
The slope of the line is the negative of the y-intercept divided by the x-intercept. The slope of a line with x and y intercept is -y-intercept/x-intercept.
What Are The Instances Where There Are No X And Y Intercepts?
There are three instances when there is no x and y-intercept for the line. If the line is parallel to the x-axis, if the line is parallel to the y-axis, and if the line is passing through the origin. The line drawn parallel to the x-axis has only the y-intercept and does not have the x-intercept. And the line drawn parallel to the y axis has only the x-intercept 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.