Reduce the following equations into intercept form and find their intercepts on the axis
(i) 3x + 2 y – 12 = 0    (ii) 4x – 3y = 6    (iii) 3y + 2 = 0

Solution:

(i) The given equation is 3x + 2y –12 = 0

It can be written as

3x + 2y = 12

3x/12 + 2y/12 = 1

x/4 + y/6 = 1 ....(1)

This equation is of the form x/a + y/b = 1 where a = 4 and b = 6.

Therefore, equation (1) is in the intercept form, where the intercepts on the x and y axes are 4 and 6 respectively.

(ii) The given equation is 4x – 3y = 6 .

It can be written as

4x/6 - 3y/6 = 1

2x/3 - y/2 = 1

x/(3/2) + y/(- 2) = 1 ....(2)

This equation is of the form x/a + y/b = 1 where a = 3/2 and b = - 2

Therefore, equation (1) is in the intercept form, where the intercepts on the x and y axes are 3/2 and - 2 respectively.

(iii) The given equation is 3y + 2 = 0

This equation has no x term. So it cannot be converted into the intercept form and hence there is no x-intercept.

The y-intercept can be found by substituting x = 0. Then we just get 3y + 2 = 0 which gives y = -2/3.

Thus, the intercept with the y-axis is -2/3 and there is no intercept with the x-axis

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.3 Question 2

Reduce the following equations into intercept form and find their intercepts on the axis. (i) 3x + 2 y – 12 = 0 (ii) 4x – 3y = 6 (iii) 3y + 2 = 0.

Summary:

i) x/4 + y/6 = 1, where the intercepts on the x and y axes are 4 and 6 respectively
ii) x/(3/2) + y/(- 2) = 1, where the intercepts on the x and y axes are 3/2 and - 2 respectively
iii) Cannot be written in intercept form, where the intercept with the y-axis is -2/3 and there is no intercept with the x-axis