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To determine the gradient, or slope, of the line segment connecting the points A(2, 3) and B(5, 11), one must apply the formula for calculating the slope between two points in a Cartesian coordinate system. The formula is expressed as (y2 – y1) / (x2 – x1), where (x1, y1) and (x2, y2) represent the coordinates of the two points. In this case, point A has coordinates (2, 3) and point B has coordinates (5, 11).
Substituting the values from the coordinates into the slope formula, we identify y2 as 11 and y1 as 3, while x2 is 5 and x1 is 2. Therefore, the calculation proceeds as follows: (11 – 3) / (5 – 2). This simplifies to 8 / 3, resulting in a gradient of 8/3 for the line segment AB. This value indicates the steepness of the line, with a positive slope suggesting that the line rises as it moves from left to right.
Understanding how to calculate the gradient is a fundamental aspect of geometry and algebra, particularly in the context of an A Level Maths Revision Course. Mastery of these concepts not only aids in solving problems related to linear equations but also enhances overall mathematical proficiency, which is essential for advanced studies in mathematics and related fields.
