An Important Question of class 10 Based on Equation of a Straight Line Chapter of M.L Aggarwal for ICSE BOARD.

You have to find the equation of the line passing through a point and intersecting a line on the y-axis.

This is the Question Number 27, Exercise 12.1 of M.L Aggarwal.

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# Find the equation of the line passing through the point (1, 4) and intersecting the line x – 2y – 11 = 0 on the y-axis.

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Given, line x – 2y – 11 = 0 passes through y-axis and point (1, 4)

So, putting x = 0 in the line equation we get the y-intercept

0 – 2y – 11 = 0

y = -11/2

The co-ordinates are (0, -11/2)

Now, the slope of the line joining the points (1, 4) and (0, -11/2) is given by

m = y

_{2}– y_{1}/ x_{2}– x_{1}= (-11/2 – 4)/ (0 – 1)

= 19/2

Thus, the line equation will be

y – y

_{1}= m (x – x_{1})y + 11/2 = 19/2 (x – 0)

2y + 11 = 19x

⇒ 19x – 2y – 11 = 0