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 = y2 – y1/ x2 – x1
= (-11/2 – 4)/ (0 – 1)
= 19/2
Thus, the line equation will be
y – y1 = m (x – x1)
y + 11/2 = 19/2 (x – 0)
2y + 11 = 19x
⇒ 19x – 2y – 11 = 0