The line through P (5, 3) intersects y-axis at Q.(i) write the slope o

1.	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 co-ordinates of Q.
Answer» (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)

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 co-ordinates of Q.

Answer»

(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)