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Complete the equation of the line through (3,-8) and (6,-4). Use exact numbers. y=

Complete the equation of the line through (3,−8) (3,-8) and (6,−4) (6,-4) .\newlineUse exact numbers.\newliney= y=

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Q. Complete the equation of the line through (3,−8) (3,-8) and (6,−4) (6,-4) .\newlineUse exact numbers.\newliney= y=
  1. Calculate slope: To find the equation of a line, we need to determine 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)(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 (3,−8)(3, -8) and (6,−4)(6, -4):\newlinem=−4−(−8)6−3=43=43m = \frac{-4 - (-8)}{6 - 3} = \frac{4}{3} = \frac{4}{3}
  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 (3,−8)(3, -8) and the slope 43\frac{4}{3} to write the equation:\newliney−(−8)=(43)(x−3)y - (-8) = \left(\frac{4}{3}\right)(x - 3)
  3. Simplify the equation: Simplify the equation by distributing the slope on the right side and moving −8-8 to the other side of the equation:\newliney+8=(43)x−(43)⋅3y + 8 = \left(\frac{4}{3}\right)x - \left(\frac{4}{3}\right)\cdot3\newliney+8=(43)x−4y + 8 = \left(\frac{4}{3}\right)x - 4\newliney=(43)x−4−8y = \left(\frac{4}{3}\right)x - 4 - 8\newliney=(43)x−12y = \left(\frac{4}{3}\right)x - 12

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