Chapters

## What is an Intercept and How to Find Intercepts?

Intercepts are the point at which the graph intersects the axes. Usually, we work in 2-dimension which means that there are two axes: the x-axis (abscissa) and y-axis (ordinate). Since intercepts are related to axes, there are two types of intercepts: x-intercept and y-intercept. If the graph crosses the x-axis, the graph's point intersects the x-axis is the x-intercept. If the graph intersects the y-axis, the graph's point intersects the y-axis is called the y-intercept. For better understanding, check the below graph:

The graph intersects both axes but which one is the x-intercept and which one is the y-intercept. The point, is the x-intercept and the point is the y-intercept. Did you notice something? The coordinates of the intercepts have their opposite axis equal to zero. Consider the x-intercept, , the y-axis is zero and the same thing is happening in the y-intercept as well. Is this an incident? No, the opposite axis should always be zero when finding the intercept. In simple words, the y-axis in the x-intercept should always be zero and the x-axis in the y-intercept should always be zero.

a is the x-intercept.

b is the y-intercept.

a and b must be nonzero.

The values of a and b can be obtained from the general form equation.

If .

If .

Imagine you are given an equation of a line, , and your teacher asks you to find the x-intercept as well as the y-intercept. The solution is pretty simple, we will find the x-intercept first, but it is your choice which intercept you want to find first. For the x-intercept, we know that the y-axis will be equal to zero. Apply this condition to the equation:

Many students make this common mistake. They finish till here but there is one thing they are missing. The question asked for the x-intercept's coordinate, therefore, end the answer with the coordinates of the respective intercept. Since we were finding the x-intercept, the final answer will be , now let's find the y-intercept.

### Some Important Points to Note

A line does not have an intercept form equation in the following cases:

1.A line parallel to the x-axis, which has the equation .

2.A line parallel to the x-axis, which has the equation .

3.A line that passes through the origin, which has equation .

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4.9 (29 reviews)
Paolo
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1st lesson free!
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Jamie
£25
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1st lesson free!
5 (16 reviews)
Harinder
£15
/h
1st lesson free!
5 (17 reviews)
Matthew
£30
/h
1st lesson free!
4.9 (12 reviews)
Petar
£40
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1st lesson free!
5 (24 reviews)
Shane
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1st lesson free!
4.9 (31 reviews)
Sehaj
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1st lesson free!

## Examples

### Example 1

A line has an x-intercept of and a y-intercept of . Find its equation.

### Example 2

The line forms a triangle with the axes. Determine the area of the triangle.

The line forms a right triangle with the origin and its legs are the axes.

If

If

The intercept form is:

The area is:

### Example 3

A line passes through the point and creates a triangle of with the axes. Determine the equation of the line.

Apply the intercept form:

The area of the triangle is:

Solve the system:

After solving simultaneously, the results are:

Therefore,

### Example 4

A line forms a triangle with the axes where the length of the leg formed by the x-axis is twice the length of the leg formed by the y-axis. If the line passes through the point , what is its equation?

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