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Complete the point-slope equation of the line through (-8,-1) and (-6,5). Use exact numbers. y-5=

Complete the point-slope equation of the line through (−8,−1)(-8,-1) and (−6,5)(-6,5). Use exact numbers.\newliney−5=y-5=

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Q. Complete the point-slope equation of the line through (−8,−1)(-8,-1) and (−6,5)(-6,5). Use exact numbers.\newliney−5=y-5=
  1. Calculate the 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 (−8,−1)(-8,-1) and (−6,5)(-6,5). 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.\newlineCalculation: m=5−(−1)−6−(−8)=62=3m = \frac{5 - (-1)}{-6 - (-8)} = \frac{6}{2} = 3
  2. Use Point-Slope Form: Now that we have the slope, we can use the point-slope form equation 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 one of the points. We can choose either point, but let's use the second point (−6,5)(-6,5) for this example.\newlineCalculation: y−5=3(x−(−6))=3(x+6)y - 5 = 3(x - (-6)) = 3(x + 6)
  3. Final Equation: The point-slope form of the equation is now y−5=3(x+6)y - 5 = 3(x + 6). This equation represents the line that passes through the points (−8,−1)(-8,-1) and (−6,5)(-6,5).

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