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
a) Write the coordinates of points A and B. Step 1: Identify the coordinates of point A from the graph. Point A is located at x=4 and y=3. Coordinates of A: (4, 3) Step 2: Identify the coordinates of point B from the graph. Point B is located at x=6 and y=-5. Coordinates of B: (6, -5) b) Determine the gradient of line AB. Step 1: Use the coordinates of points A and B. Let A = (x_1, y_1) = (4, 3) Let B = (x_2, y_2) = (6, -5) Step 2: Apply the gradient formula. The gradient m is given by the formula: m = (y_2 - y_1)/(x_2 - x_1) Step 3: Substitute the coordinates into the formula. m = (-5 - 3)/(6 - 4) m = (-8)/(2) m = -4 The gradient of line AB is -4. c) Determine the equation of line AB in the form y = mx + c. Step 1: Use the gradient m = -4 (from part b) and one of the points, for example, point A (4, 3). The equation of a line can be written in the point-slope form: y - y_1 = m(x - x_1). Step 2: Substitute the gradient and the coordinates of point A into the point-slope form. y - 3 = -4(x - 4) Step 3: Simplify the equation to the form y = mx + c. y - 3 = -4x + (-4)(-4) y - 3 = -4x + 16 y = -4x + 16 + 3 y = -4x + 19 The equation of line AB is y = -4x + 19.