GCSE Maths Practice: coordinates

The gradient of a line shows how steep it is and is calculated by dividing the change in y-coordinates by the change in x-coordinates between two points. Using the formula m = (y2 - y1)/(x2 - x1), we find the gradient for any two points. For example, between points (2,3) and (6,11), the difference in y is 11-3=8, and the difference in x is 6-2=4. Dividing gives 8/4=2. The gradient tells us that for every 1 unit increase in x, y increases by 2 units. Gradients can be positive, negative, zero, or undefined. Positive means the line rises, negative means it falls, zero is horizontal, and undefined is vertical. Understanding gradient helps in solving problems with parallel and perpendicular lines, equations of lines, and graph sketching. It also forms the basis for further concepts such as rate of change and linear relationships. Practice by plotting points and drawing lines to visually see how gradient represents slope. Gradients also help check the accuracy of plotted graphs and are essential when finding the equations of straight lines passing through points. Consistent practice ensures confidence in identifying and calculating gradients quickly.