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Complete the point-slope equation of the line through (-1,6) and (1,5). Use exact numbers. y-6= ◻

Complete the point-slope equation of the line through (−1,6)(-1,6) and (1,5)(1,5). Use exact numbers.\newliney−6=y-6=

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Full solution

Q. Complete the point-slope equation of the line through (−1,6)(-1,6) and (1,5)(1,5). Use exact numbers.\newliney−6=y-6=
  1. Calculate slope using formula: Calculate the slope mm of the line using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}, where (x1,y1)=(−1,6)(x_1, y_1) = (-1, 6) and (x2,y2)=(1,5)(x_2, y_2) = (1, 5).\newlineCalculation: m=5−61−(−1)=−12m = \frac{5 - 6}{1 - (-1)} = \frac{-1}{2}
  2. Write point-slope form equation: Write the point-slope form equation using one of the points and the slope. We'll use the point (−1,6)(-1, 6).\newlineCalculation: y−6=(−12)(x−(−1))y - 6 = \left(-\frac{1}{2}\right)(x - (-1))
  3. Simplify the equation: Simplify the equation.\newlineCalculation: y−6=(−12)(x+1)y - 6 = \left(-\frac{1}{2}\right)(x + 1)

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