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Point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is slope and (x1,y1)(x_1, y_1) is a point on the line. With m=−23m = -\tfrac{2}{3} and (x1,y1)=(6,1)(x_1, y_1) = (6, 1), substitute directly to get y−1=−23(x−6)y - 1 = -\tfrac{2}{3}(x - 6). That is option A. Option B incorrectly adds signs to both yy and xx, implying a point at (−6,−1)(-6,-1). Option C swaps the roles of xx and yy in the offsets, placing the point at (1,6)(1,6). Option D again reflects wrong signs and coordinates. After establishing point-slope, you can convert to slope-intercept for checking: distribute −23-\tfrac{2}{3}: y−1=−23x+4y - 1 = -\tfrac{2}{3}x + 4. Then add 1: y=−23x+5y = -\tfrac{2}{3}x + 5. Verify by plugging in x=6x=6: y=−23(6)+5=−4+5=1y = -\tfrac{2}{3}(6) + 5 = -4 + 5 = 1, which matches the given point. On PERT, recognizing when point-slope is faster than slope-intercept saves time, especially when a convenient point is provided. The key is sign discipline: y−y1y - y_1 and x−x1x - x_1 must reflect exact coordinates.