Question

Find the gradient of the line joining (3, 1) and (6, 4).

Answer 1

The gradient of a line is defined as the ratio of the change in y to the change in x. The change in y from point to point is 3 since the y-coordinate of the line goes from 1 to 4:

$4-1=3$

Similarly, the change in x from point to point is also 3, since the x-coordinate goes from 3 to 6:

$6-3=3$

Then, being the gradient the ratio of the above quantities:

$\frac{3}{3}=1$

We have that the gradient of a line joining points (3, 1) and (6, 4) is 1.