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A straight line passes through the points A(-5, 2) and B(3,-6). It intersects the co-ordinate axes at points C and D . Find :
the equation of AB.

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To find the equation of the line passing through the points A(-5, 2) and B(3, -6), we will follow these steps: ### Step 1: Identify the coordinates of points A and B - A = (-5, 2) - B = (3, -6) ### Step 2: Calculate the slope (m) of the line AB The formula for the slope (m) between two points (x1, y1) and (x2, y2) is given by: \[ m = \frac{y2 - y1}{x2 - x1} \] Substituting the coordinates of points A and B: - x1 = -5, y1 = 2 - x2 = 3, y2 = -6 Now, substituting these values into the slope formula: \[ m = \frac{-6 - 2}{3 - (-5)} \] \[ m = \frac{-8}{3 + 5} \] \[ m = \frac{-8}{8} \] \[ m = -1 \] ### Step 3: Use the point-slope form of the equation of a line The point-slope form of the equation of a line is: \[ y - y1 = m(x - x1) \] Using point A(-5, 2) and the slope m = -1: \[ y - 2 = -1(x - (-5)) \] \[ y - 2 = -1(x + 5) \] ### Step 4: Simplify the equation Distributing the -1: \[ y - 2 = -x - 5 \] Now, adding 2 to both sides: \[ y = -x - 5 + 2 \] \[ y = -x - 3 \] ### Step 5: Rearranging to standard form To express the equation in standard form (Ax + By + C = 0): \[ x + y + 3 = 0 \] ### Final Equation Thus, the equation of the line AB is: \[ x + y + 3 = 0 \] ---
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