In this page equation of line solution7 we are going to see solution of each problem with detailed explanation of the worksheet slope of the line.

(13) Find the equation of the straight line passing through the point (3 , 4) and has intercepts which are in the ratio 3 :2

**Solution:**

Intercept form:

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

here intercepts are in the ratio 3 : 2

So x-intercept (a) = 3 t

y-intercept (b) = 2 t

(3/3t) + (4/2t) = 1

(1/t) + (2/t) = 1

3/t = 1

3 = t

t = 3

So,x-intercept (a) = 3 t = 3 (3) = 9

y-intercept (b) = 2 t = 2 (3) = 6

(x/9) + (y/6) = 1

(2 x + 3 y)/18 = 1

2 x + 3 y = 18

2 x + 3 y - 18 = 0

(14) Find the equation of the straight lines passing through the point (2,2) and sum of the intercepts is 9.

**Solution:**

Intercept form:

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

Sum of intercept = 9

a + b = 9

b = 9 - a

The required line is passing through the point (2,2)

(2/a) + (2/9-a) = 1

[2 (9 - a) + 2 a]/[a(9 - a)] = 1

[18 - 2 a + 2a]/9a - a² = 1

18/9a - a² = 1

18 = 9a - a²

a² - 9 a + 18 = 0

(a - 3) (a - 6) = 0

a = 3 and a = 6

Substitute a = 3 and a = 6 in the equation b = 9 - a

b = 9 - 3 b = 9 - 6

b = 6 b = 3

a = 3 , b = 6

(x/3) + (y/6) = 1

(2 x + y)/6 = 1

2 x + y = 6

2 x + y - 6 = 0

a = 6 , b = 3

(x/6) + (y/3) = 1

(x + 2y)/6 = 1

x + 2y = 6

x + 2 y - 6 = 0

Therefore the required equations are 2 x + y - 6 = 0 or x + 2 y - 6 = 0

(15) Find the equation of the straight line passing through the point (5,-3) and whose intercepts on the axes are equal in magnitude but opposite in sign.

**Solution:**

Intercept form:

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

intercepts are equal in magnitude but opposite in sign.

x-intercept (a) = t

y-intercept (b) = -t

The required line is passing through the point (5,-3)

(5/t) + (-3/(-t)) = 1

(5/t) + (3/t) = 1

(5 + 3)/t = 1

8/t = 1

8 = t

t = 8

(x/8) + (y/(-8)) = 1

(x - y)/8 = 1

x - y = 8

x - y - 8 = 0

equation of line solution7 equation of line solution7