We are going to discover the equation of a line whose intercepts are ‘a’ and ‘b’ on the coordinate axes respectively.

Let PQ be a line assembly X axis at A and Y axis at B.

Let OA = a, OB = b. Then the coordinates of A and B are (a, 0) and (0, b) respectively.Â

Due to this fact, the equation of the road becoming a member of A and B is

Utilizing two-point type, equation of line becoming a member of the 2 factors A and B is

(y – 0)/(b – 0) = (x – a)/(0 – a)

y/b = -(x – a)/a

y/b = (-x + a)/a

y/b = -x/a + 1

Therefore, Intercept-Kind equation of a line isÂ

x/a + y/b = 1

Instance 1 :

If the x-intercept and y-intercept of a straight line are 2 and -4 respectively, discover the final equation of the straight line.

Resolution :

Given :Â x- intercept is 2 and y-intercept is -4.

Equation of a straight line in intercept type :

x/a Â + Â y/b = 1

Substitute a = 2 and b = -4.

x/2 + y/(-4) = 1

x/2 – y/4 = 1

Least frequent a number of of the denominators 2 and 4 is 4.

Multiply both sides by 4 to eliminate the fractions.

2x – y = 4

Subtract 4 from both sides.

2x – y – 4 = 0

Instance 2 :

Discover the intercepts made by the road 4x + 9y – 36 = 0 on the coordinate axes.

Resolution :

Write the equation in intercept type.

4x + 9y – 36 = 0

Add 36 to every aspect.

4x + 9y = 36

Divide both sides by 36.

(4x + 9y)/36 = 36/36

4x/36 + 9y/36 = 1

x/9 + y/4 = 1

x-intercept = 9

y-intercept = 4

Instance 3 :

Discover the equation of a line in commonplace type which passes by way of (7, 5) and makes intercepts on the axes equal in magnitude however reverse in signal.

Resolution :

Let ‘a’ the x-intercept of the road.

Then y-intercept is ‘-a’.

Equation of line in intercept type :

x/a + y/b = 1

Substitute b = -a.

x/a + y/(-a) = 1

x/a – y/a = 1

(x – y)/a = 1

x – y = a —-(1)

The road is passing by way of the purpose (7, 5).

So, substitute x = 7 and y = 5.

7 – 5 = a

2 = a

Substitute a = 2 in (1).

x – y = 2

Instance 4 :

A line makes constructive intercepts on coordinate axes whose sum is 7 and it passes by way of (-3, 8) . Discover the equation of line in commonplace type.

Resolution :

Let ‘a’ and ‘b’ be the intercepts.

a + b = 7

b = 7 – a

Intercept-form equation of a line :

x/a + y/b = 1

Substitute b = 7 – a.

x/a + y/(7 – a) = 1

â€“3(7 â€“ a) + 8a = a(7 â€“ a)

-21 + 3a + 8a = 7a – a^{2}

a^{2} + 4a – 21 = 0

(a – 3)(a + 7) = 0

a = 3 or a = -7

Since a is constructive,

a = 3

b = 7 â€“ a = 7 â€“ 3 = 4

Equation of line :

x/3 + y/4 = 1

Least frequent a number of of the denominators 3 and 4 is 12.Â

Multiply both sides by 12 to eliminate the fractions.

4x + 3y = 12

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