We have all encountered gradients in our everyday life. Walking uphill is when we walk on ground with a positive gradient, and for downhill the ground has a negative gradient, and flat ground has zero gradient. You can click on the buttons to view lines with positive and negative gradients. The rise from A to B is the change of the y-coordinate, which for negative gradients is a negative value. The run is the change of the x-coordinate from A to B, and is always positive value except for vertical lines.

The gradient of the line from A to B is the ratio of the the "rise" and the "run" :

The equation of the line though the two points shown below can be found algebraically

Determine the equation of the lines through these points:

m

numerator

denominator

'

numerator

denominator

'

c

numerator

denominator

numerator

denominator

check you working out below:

(1) Positive gradients have positive values of m and negative gradients have negative values of m.

(2) The equation of straight line though two points can be found by first calculating the rise and the run. The gradient m is the ratio of the rise and run. The c value can be found by inputing the x and y values into the equation of the line and then solving for c.