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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 = \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 = \square
  1. Calculate Slope: To find the point-slope form of the equation of a line, we first need to calculate the slope of the line using the two given points (−1,6)(-1,6) and (1,5)(1,5). The slope mm is given by the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of the two points.
  2. Substitute Coordinates: Substitute the coordinates of the points into the slope formula: m=5−61−(−1)=−12=−12m = \frac{5 - 6}{1 - (-1)} = \frac{-1}{2} = -\frac{1}{2}.
  3. Apply Point-Slope Form: Now that we have the slope, we can use the point-slope form of the equation of a line, which is y−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line. We can use either of the two points given, but let's use the point (−1,6)(-1,6).
  4. Final Equation: Substitute the slope and the coordinates of the point into the point-slope form: y−6=(−12)(x−(−1))=(−12)(x+1)y - 6 = \left(-\frac{1}{2}\right)(x - (-1)) = \left(-\frac{1}{2}\right)(x + 1).

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