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Complete the equation of the line through (4,-8) and (8,5). Use exact numbers. y=

Complete the equation of the line through (4,−8) (4,-8) and (8,5) (8,5) .\newlineUse exact numbers.\newliney= y=

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Q. Complete the equation of the line through (4,−8) (4,-8) and (8,5) (8,5) .\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 (4,−8)(4, -8) and (8,5)(8, 5).\newlinem=5−(−8)8−4=134m = \frac{5 - (-8)}{8 - 4} = \frac{13}{4}
  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 (4,−8)(4, -8) and the slope 134\frac{13}{4} to write the equation.\newliney−(−8)=(134)(x−4)y - (-8) = \left(\frac{13}{4}\right)(x - 4)
  3. Simplify the equation: Simplify the equation by distributing the slope on the right side and moving the −8-8 to the other side of the equation.\newliney+8=(134)x−(134)⋅4y + 8 = \left(\frac{13}{4}\right)x - \left(\frac{13}{4}\right)\cdot4\newliney+8=(134)x−13y + 8 = \left(\frac{13}{4}\right)x - 13\newliney=(134)x−13−8y = \left(\frac{13}{4}\right)x - 13 - 8\newliney=(134)x−21y = \left(\frac{13}{4}\right)x - 21

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