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Write the equation of the line that passes through the points (-4,9) and (2,-8). 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 (−4,9) (-4,9) and (2,−8) (2,-8) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:

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Q. Write the equation of the line that passes through the points (−4,9) (-4,9) and (2,−8) (2,-8) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Calculate slope: Calculate the slope mm of the line using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. We have the points (−4,9)(-4,9) and (2,−8)(2,-8). Let's denote (−4,9)(-4,9) as (x1,y1)(x_1,y_1) and (2,−8)(2,-8) as (x2,y2)(x_2,y_2). Using the slope formula: m=−8−92−(−4)m = \frac{-8 - 9}{2 - (-4)} m=−176m = \frac{-17}{6} m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}00
  2. Write point-slope form: Write the point-slope form of the equation of the line.\newlineThe point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1).\newlineWe can use either of the two points for (x1,y1)(x_1,y_1). Let's use the first point (−4,9)(-4,9).\newlineSubstitute m=−176m = -\frac{17}{6} and the point (−4,9)(-4,9) into the equation.\newliney−9=(−176)(x−(−4))y - 9 = \left(-\frac{17}{6}\right)(x - (-4))\newliney−9=(−176)(x+4)y - 9 = \left(-\frac{17}{6}\right)(x + 4)
  3. Simplify equation: Simplify the equation if necessary.\newlineIn this case, the equation is already in point-slope form and does not need further simplification.

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