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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) .\newlineUse exact numbers.\newliney−6= y-6= \newline□ \square

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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) .\newlineUse exact numbers.\newliney−6= y-6= \newline□ \square
  1. Calculate slope: 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).\newlinem=5−61−(−1)=−12=−12m = \frac{5 - 6}{1 - (-1)} = \frac{-1}{2} = -\frac{1}{2}.
  2. Use point-slope form: Use the point-slope form equation y−y1=m(x−x1)y - y_1 = m(x - x_1) with one of the points and the slope. Let's use the point (−1,6)(-1, 6).\newliney−6=(−12)(x−(−1))y - 6 = \left(-\frac{1}{2}\right)(x - (-1)).
  3. Simplify equation: Simplify the equation. y−6=(−12)(x+1).y - 6 = \left(-\frac{1}{2}\right)(x + 1).

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