GCSE Maths Practice: coordinates

To determine the equation of a line, we use y=mx+c where m is the gradient and c is the y-intercept. The gradient m measures the steepness of the line, calculated as the ratio of the vertical change to the horizontal change between two points. Once we know the gradient and a point through which the line passes, we can find c by substituting the coordinates of the point into the equation and solving for c. For example, if the gradient is 2 and the line passes through (0,3), substituting x=0 and y=3 gives c=3, so the line equation is y=2x+3. It's important to understand that the gradient indicates the slope direction: a positive gradient rises to the right, a negative falls, zero is horizontal, and undefined is vertical. Practice with lines through different points and gradients helps build understanding. Additionally, learning to manipulate the equation allows solving for x or y given a coordinate. This process forms the foundation for more advanced coordinate geometry problems including parallel and perpendicular lines, line intersections, and graphing linear equations accurately. Developing fluency with this method ensures success across all topics involving straight-line graphs.