Question

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

Answer 1

Answer:

The gradient of the line joining the points $P(x,y) = (2,3)$ and $Q(x,y) = (5,7)$ is $\frac{4}{3}$.

Step-by-step 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:

$m_{PQ} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}$ (1)

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

$m_{PQ} = \frac{7-3}{5-2}$

$m_{PQ} = \frac{4}{3}$

The gradient of the line joining the points $P(x,y) = (2,3)$ and $Q(x,y) = (5,7)$ is $\frac{4}{3}$.