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
Here is the solution for finding the slope of the line for each pair of points. The formula for the slope m of a line passing through two points (x_1, y_1) and (x_2, y_2) is: m = (y_2 - y_1)/(x_2 - x_1) a) For the points (-4, 6) and (4, 3) Step 1: Assign the coordinates. Let (x_1, y_1) = (-4, 6) Let (x_2, y_2) = (4, 3) Step 2: Substitute the values into the slope formula. m = (3 - 6)/(4 - (-4)) Step 3: Simplify the expression. m = (-3)/(4 + 4) m = (-3)/(8) The slope for part a) is -(3)/(8). b) For the points (5, 4) and (6, -4) Step 1: Assign the coordinates. Let (x_1, y_1) = (5, 4) Let (x_2, y_2) = (6, -4) Step 2: Substitute the values into the slope formula. m = (-4 - 4)/(6 - 5) Step 3: Simplify the expression. m = (-8)/(1) m = -8 The slope for part b) is -8.