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
Step 1: Identify the coordinates of the two given points. The points are P(x_1, y_1) = (1, -(1)/(2)) and Q(x_2, y_2) = (3, -8(1)/(2)). Step 2: Convert the mixed fraction to an improper fraction. y_2 = -8(1)/(2) = -((8 × 2) + 1)/(2) = -(16 + 1)/(2) = -(17)/(2). Step 3: Use the formula for the gradient (slope) of a line passing through two points (x_1, y_1) and (x_2, y_2): m = (y_2 - y_1)/(x_2 - x_1) Step 4: Substitute the coordinates into the formula. m = (-17)/(2) - (-(1)/(2))3 - 1 Step 5: Simplify the numerator. -(17)/(2) - (-(1)/(2)) = -(17)/(2) + (1)/(2) = (-17 + 1)/(2) = (-16)/(2) = -8 Step 6: Simplify the denominator. 3 - 1 = 2 Step 7: Calculate the gradient. m = (-8)/(2) = -4 The gradient of the line passing through points P and Q is: -4