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
11. a) A line passes through the points (2, 3) and (4, 7). Find the equation of the line. Step 1: Calculate the gradient (slope) m using the formula m = (y_2 - y_1)/(x_2 - x_1). Given points are (x_1, y_1) = (2, 3) and (x_2, y_2) = (4, 7). m = (7 - 3)/(4 - 2) m = (4)/(2) m = 2 Step 2: Use the point-slope form of a linear equation, y - y_1 = m(x - x_1), with one of the points, for example, (2, 3), and the calculated gradient m=2. y - 3 = 2(x - 2) Step 3: Simplify the equation to the slope-intercept form y = mx + c. y - 3 = 2x - 4 y = 2x - 4 + 3 y = 2x - 1 The equation of the line is y = 2x - 1. 3 done, 2 left today. You're making progress.