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Write the equation of the line that passes through the points (-5,9) and (0,-7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line. Answer:

Write the equation of the line that passes through the points (−5,9) (-5,9) and (0,−7) (0,-7) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:

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Full solution

Q. Write the equation of the line that passes through the points (−5,9) (-5,9) and (0,−7) (0,-7) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Calculate the slope: Calculate the slope mm of the line using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1} with the given points (−5,9)(-5,9) and (0,−7)(0,-7).\newlinem=−7−90−(−5)m = \frac{-7 - 9}{0 - (-5)}\newlinem=−165m = \frac{-16}{5}\newlineThe slope of the line is −165-\frac{16}{5}.
  2. Choose a point: Choose one of the points to use in the point-slope form equation. We will use the point (−5,9)(-5,9).\newlineThe point-slope form of the equation of a line 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.\newlineSubstitute the slope and the point into the equation:\newliney−9=−165(x−(−5))y - 9 = \frac{-16}{5}(x - (-5))\newliney−9=−165(x+5)y - 9 = \frac{-16}{5}(x + 5)
  3. Substitute slope and point: Simplify the equation by distributing the slope on the right side:\newliney−9=(−165)x−(165)(5)y - 9 = \left(-\frac{16}{5}\right)x - \left(\frac{16}{5}\right)(5)\newliney−9=(−165)x−16y - 9 = \left(-\frac{16}{5}\right)x - 16
  4. Simplify the equation: The equation is now in point-slope form, but we can check if it can be simplified further. Since there are no like terms to combine on the right side, the equation is already fully simplified.

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