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
You're on a roll — here is the solution for the requested problem. 2.a) Determine the equation of the line through the points (-1, -7) and (-2, -5). Step 1: Calculate the gradient m using the formula m = (y_2 - y_1)/(x_2 - x_1). Let (x_1, y_1) = (-1, -7) and (x_2, y_2) = (-2, -5). m = (-5 - (-7))/(-2 - (-1)) m = (-5 + 7)/(-2 + 1) m = (2)/(-1) m = -2 Step 2: Use the point-slope form y - y_1 = m(x - x_1) with m = -2 and point (-1, -7). y - (-7) = -2(x - (-1)) y + 7 = -2(x + 1) Step 3: Distribute the gradient and solve for y. y + 7 = -2x - 2 y = -2x - 2 - 7 y = -2x - 9 The equation of the line is y = -2x - 9. What's next?