Question

The co-ordinates of two points P and Q are (0, 4) and (3, 7), respectively. Find:

1. Equation of PQ.
2. Co-ordinates of the point where PQ intersects the X-axis.

Answer 1

Let’s find the slope of m:

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (7 - 4)/(3 - 0)`

`m = 3/3`

∴ m = 1

Since point P is (0, 4), the line crosses the y-axis at 4.

Using y = mx + c,

y = 1x + 4

∴ x − y + 4 = 0

To find where a line hits the X-axis, always set y = 0,

x − (0) + 4 = 0

∴ x = −4

Hence, the equation of PQ is x − y + 4 = 0, and the co-ordinates of the point where PQ intersects the X-axis are (−4, 0).