# Write down the equation of the line whose gradient is 3/2 and which passes through P where P divides the line segment joining A (– 2, 6) and B (3, – 4) in the ratio 2 : 3.

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This question is Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
Here Given that:
A Gradient which passes through a point and that point divided a line segment joining two points in a ratio
Find out the equation of the line.
This is the Question Number 26, Exercise 12.1 of M.L Aggarwal.

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### 1 Answer

1. Given, P divides the line segment joining the points A (-2, 6) and B (3, -4) in the ratio 2: 3

So, the co-ordinates of P will be

x = (m1x2 + m2x1)/(m1 + m2)

= (2×3 + 3×(-2))/ (2 + 3)

= (6 – 6)/5

= 0/5 = 0

y = (m1y2 + m2y1)/(m1 + m2)

= (2×(-4) + 3×(6))/ (2 + 3)

= (-8 + 18)/5 = 10/5

= 2

Hence, the co-ordinates of P are (0, 2)

Now, the slope (m) of the line passing through (0, 2) is 3/2

Thus, the equation will be

y – y1 = m (x – x1)

y – 2 = 3/2 (x – 0)

2y – 4 = 3x

⇒ 3x – 2y + 4 = 0

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