Question

The line through P(5, 3) intersects y-axis at Q.

1. Write the slope of the line.
2. Write the equation of the line.
3. Find the co-ordinates of Q.

Answer 1

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)