Question

Work out the gradient of the line joining the points (2, 3) and (5,7)

Answer 1

The gradient of the line joining the points
`P(x,y) = (2,3)` and
`Q(x,y) = (5,7)` is
`(4)/(3)`.

Explanation:

The gradient of the line joining two distinct point on a plane is represented by the slope of a secant line (
`m_(PQ)`), that is:

`m_(PQ) = (y_(Q)-y_(P))/(x_(Q)-x_(P))` (1)

If we know that
`P(x,y) = (2,3)` and
`Q(x,y) = (5,7)`, then the gradient of the line is:

`m_(PQ) = (7-3)/(5-2)`

`m_(PQ) = (4)/(3)`

The gradient of the line joining the points
`P(x,y) = (2,3)` and
`Q(x,y) = (5,7)` is
`(4)/(3)`.