The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the x-axis, then it is called the x-intercept. If a point crosses the y-axis, then it is called the y-intercept.

## Intercept Formula

The equation of the line, which intersects the y-axis at a point is given by:**y = mx + c**

Now, we have to write the intercept form of the line, we can replace c with b. Thus, the equation becomes:

**y = mx + b**

Hence, the formula for the y-intercept of a line is given by:**b = y – mx**

Where b is the intercept, m is the slope of the line and y and x indicate the points on the y-axis and x-axis respectively.

Now, another way of writing the equation of the line, considering a line is intersecting the x-axis and y-axis at points a and b respectively.**x/a + y/b = 1**

Here, a and b are the intercepts of the line which intersect the x-axis and y-axis, respectively. The values of a and b can be positive, negative or zero and explain the position of the points at which the line cuts both axes, relative to the origin.

### Solution

The line cuts off equal intercepts on the coordinate axes i.e. a = b.

We know that equation of the line intercepts a and b on the x-and y-axis, respectively, which is

x/a + y/b = 1

So, x/a + y/a = 1

x + y = a … (1)

Given: point (2, 3)

2 + 3 = a

a = 5

Substitute value of ‘a’ in (1), we get

x + y = 5

x + y – 5 = 0

∴ The equation of the line is x + y – 5 = 0.