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Write the equation of the line that passes through the points (1,6) and (-7,8). 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 (1,6) (1,6) and (−7,8) (-7,8) . 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 (1,6) (1,6) and (−7,8) (-7,8) . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.\newlineAnswer:
  1. Calculate slope: First, 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 (1,6)(1,6) and (−7,8)(-7,8).\newlinem=8−6−7−1m = \frac{8 - 6}{-7 - 1}\newlinem=2−8m = \frac{2}{-8}\newlinem=−14m = -\frac{1}{4}
  2. Write point-slope equation: Now that we have the slope, we can use one of the points and the slope to write the equation in point-slope form, which is y−y1=m(x−x1)y - y_1 = m(x - x_1). Let's use the point (1,6)(1,6). \newliney−6=(−14)(x−1)y - 6 = \left(-\frac{1}{4}\right)(x - 1)
  3. Final form: The equation y−6=(−14)(x−1)y - 6 = \left(-\frac{1}{4}\right)(x - 1) is already in point-slope form and does not need further simplification. It is not a vertical or horizontal line, so this is the final form.

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