GCSE Maths Practice: coordinates
This question teaches finding the equation of a line parallel to a given line passing through a specific point.
Keep the same gradient as the original line. Substitute the given point to find c.
Parallel lines have equal gradients. If you know the gradient of the original line and a point through which the new line passes, you can find the y-intercept of the new line. For example, a line y=3x+5 has gradient 3. A line parallel to it through (0,2) has the same gradient, so y=3x+c. Substitute x=0, y=2 to solve for c: 2=3*0+c, giving c=2. Hence, y=3x+2. Understanding parallel lines is critical in coordinate geometry for constructing shapes, graph analysis, and solving intersection problems. Practice with different gradients and points helps solidify the relationship between gradient and y-intercept. This skill is used in real-world applications like design, engineering, and navigation. Graphing the lines also helps visualize how lines maintain equal spacing and never intersect.