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complete the equation of the line through (6,−6)(6,-6) and (8,8)(8,8)

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Full solution

Q. complete the equation of the line through (6,−6)(6,-6) and (8,8)(8,8)
  1. Calculate Slope: To find the equation of a line, we need to determine the slope mm of the line using the slope 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 given points.\newlineLet's calculate the slope using the points (6,−6)(6, -6) and (8,8)(8, 8).\newlinem=8−(−6)8−6=142=7m = \frac{8 - (-6)}{8 - 6} = \frac{14}{2} = 7
  2. Use 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.\newlineLet's use the point (6,−6)(6, -6) and the slope 77 to write the equation.\newliney−(−6)=7(x−6)y - (-6) = 7(x - 6)
  3. Simplify Equation: Simplify the equation by distributing the slope and moving −6-6 to the other side of the equation.\newliney+6=7x−42y + 6 = 7x - 42\newliney=7x−42−6y = 7x - 42 - 6\newliney=7x−48y = 7x - 48

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