This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Part (b) Step 1: The formula for the gradient m of a line passing through two points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1) Step 2: The points are (x_1, y_1) = (2, 3) and (x_2, y_2) = (4, 7). Substitute the values: m = (7 - 3)/(4 - 2) Step 3: Simplify: m = (4)/(2) = 2 The gradient is 2. Part (c) Step 1: The formula for the gradient m of a line passing through two points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1) Step 2: The points are (x_1, y_1) = (3, 5) and (x_2, y_2) = (6, 11). Substitute the values: m = (11 - 5)/(6 - 3) Step 3: Simplify: m = (6)/(3) = 2 The gradient is 2.