(i) The equation of the y-axis is x = 0
Given that the required line through P (5, 3)
Intersects the y-axis at Q and the angle of inclination is 45°
Therefore slope of the line PQ = tan 45° = 1
(ii) The equation of a line passing through the point
A(x1, y1) with slope ‘m’ is
y – y1 = m (x – x1)
Therefore, the equation of the line passing
through the point P (5, 3) with slope 1 is
y -3 = 1 ×(x – 5)
⇒ y – 3 = x – 5
⇒ x – y = 2
(iii) From subpart (ii), the equation of the line PQ
Is x – y = 2
Given that the line intersects with the y – axis, x = 0
Thus, substituting x = 0 in the equation x – y = 2
We have, 0 – y = 2
⇒ y = − 2
Thus, the coordinates point of intersection Q
Are q(0, −2)