Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3)

Solution:

The equation of the line in the intercept form is

x/a + y/b = 1 ....(1)

Here, a and b are the intercepts on x and y axes respectively.

It is given that the line cuts off equal intercepts on both axes. This means that a = b.

Accordingly, equation (1) reduces to

x + y = a ....(2)

Since the given line passes through point (2, 3), equation (2) reduces to

2 + 3 = a

a = 5

On substituting the value of a in equation (2), we obtain

x + y = 5, which is the required equation of the line

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Question 12

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the points (2, 3).

Summary:

The equation of a line that cuts off equal intercepts on the coordinate axes and passes through the points (2, 3) is x + y = 5