This question is Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD for class 10.

The line through a point intersects y-axis at a point So,find the slope of the line ,equation of the line, coordinates of Q.

This is the Question Number 29, Exercise 12.2 of M.L Aggarwal.

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# The line through P (5, 3) intersects y-axis at Q. (i) Write the slope of the line. (ii) Write the equation of the line. (iii) Find the coordinates of Q.

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(i) Here, θ = 45

^{o}So, the slope of the line = tan θ = tan 45

^{o}= 1(ii) Equation of the line through P and Q is

y – 3 = 1(x – 5)

x – y – 2 = 0

(iii) Let the co-ordinates of Q be (0, y)

Then, m = y

_{2}– y_{1}/ x_{2}– x_{1}1 = (3 – y)/ (5 – 0)

5 = 3 – y

y = 3 – 5 = -2

Thus, co-ordinates of Q are (0, -2).