Intercepts of a line on the X and Y Axes

Intercept Form

x/a + y/b = 1 represents the intercept form of the equation. The intercept form is considered the important form of the equation in maths. The symbol (+ve and -ve) of intercepts in the equation assists us to find the line in the graph. A right triangle is created from the intercept form in coordinate axes having a and b as the length of sides which is also a method to understand the concept.

So now we will see the equation associated with it, derivation of the equation and graphical representation in order to understand more

What Is Intercept Form?

x/a + y/b = 1 represents a form of equation in which a is called intercept of x and b is called intercept of y.  Intercept of x is the minimum length of a point from the origin to Abscissa. Along with that Intercept of x is a position where the line slashes the Abscissa. The intercept of y is the minimum length of a point from the origin to Ordinate. And the intercept of y is a position where the line slashes Ordinate. The line slashes the Abscissa is (a,0), and the coordinate is (b,0).

Equation of a Line : x/a + y/b = 1.

In which the variables of the equation are x and y. The a is known as the intercept of x and b is known as  intercept of y. And the slope in the given equation is represented by -b/a.

The line which slashes two coordinate axes i.e. x and y also creates a right triangle with axes. We can find the area by  ½ of its intercepts.

½ X a X b.  

For the line equation, we can also write it as bx+ay=ab in a simplified form.

Graphical representation 

In the graph, the line slashes the axes at both points at x and y axes. These points at  x and y axes  have length of a and b units from the centre or the origin. The line also slashes the Abscissa having length a distances,  which is represented by  (a,0) . Similarly, the same line slashes  the Ordinate having length b distances, which is represented by (0,b).

Let us derive the equation 

We can derive the equation of a given line from another form. Mainly two point form will be used to derive the intercept form of the equation.

Derivation

This derivation requires two points on the cartesian plane. In the abscissa it is (a,0) and in the ordinate it is (0,b) are taken as two points for derivation.

y – 0 = (b – 0)/(0 – a).(x – a)

y = b/-a.(x – a)

-ay = b(x – a)

-ay = bx – ab

ab = bx + ay

bx + ay = ab

(bx + ay)/ab = 1

bx/ab + ay/ab = 1

x/a + y/b = 1

Given below are some of the points which will help us to clearly understand the concept

1. x/a + y/b = 1 represents a form of equation.
2. In which a is called intercept of x and b is called intercept of y. 
3. Intercept of x is the minimum length of a point from the origin to Abscissa. 
4. The intercept of y is the minimum length of a point from the origin to Ordinate.
5. The line which slashes two coordinate axes i.e. x and y also creates a right triangle with axes. We can find the area by  ½ of its intercepts.
6. ½ X a X b

Conclusion

In this article we have discussed the intercept form of the equation of a line which is x/a + y/b = 1 represents a form of equation in which a is called intercept of x and b is called intercept of y.  Intercept of x is the minimum length of a point from the origin to Abscissa. Along with that Intercept of x is a position where the line slashes the Abscissa. The intercept of y is the minimum length of a point from the origin to Ordinate. And the intercept of y is a position where the line slashes Ordinate. The line slashes the Abscissa is (a,0), and the coordinate is (b,0).

In which the variables of the equation are x and y. The a is known as the intercept of x and b is known as  intercept of y. And the slope in the given equation is represented by -b/a.The line which slashes two coordinate axes i.e. x and y also creates a right triangle with axes. We can find the area by  ½ of its intercepts.

½ X a X b.