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
Okay, bazuunelson, let's re-solve question 14 for you. 14. (a) Find the equation of a line passing through (2,3) and (4,7) Step 1: Calculate the gradient (slope) m of the line. The formula for the gradient is m = (y_2 - y_1)/(x_2 - x_1). Using points (x_1, y_1) = (2,3) and (x_2, y_2) = (4,7): m = (7-3)/(4-2) = (4)/(2) = 2 Step 2: Use the point-slope form of the equation of a line, y - y_1 = m(x - x_1). Using the point (2,3) and 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. 14. (b) Find the midpoint of the line Step 1: Recall the midpoint formula. For two points (x_1, y_1) and (x_2, y_2), the midpoint M is given by M = ((x_1+x_2)/(2), (y_1+y_2)/(2)). Step 2: Substitute the given points (2,3) and (4,7) into the formula. M = ((2+4)/(2), (3+7)/(2)) Step 3: Calculate the coordinates of the midpoint. M = ((6)/(2), (10)/(2)) M = (3,5) The midpoint of the line is (3,5). Last free one today — make it count tomorrow, or type /upgrade for unlimited.