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Write the equation of the line that passes through the points (6,6) and (7,-5). 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 (6,6) (6,6) and (7,−5) (7,-5) . 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 (6,6) (6,6) and (7,−5) (7,-5) . 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}. Given points: (6,6)(6,6) and (7,−5)(7,-5). Slope mm = −5−67−6=−111=−11\frac{-5 - 6}{7 - 6} = \frac{-11}{1} = -11.
  2. Use point-slope form: Use the point-slope form of the equation of a line: 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 (6,6)(6,6).\newlinePoint-slope form: y−6=−11(x−6)y - 6 = -11(x - 6).
  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.\newlineFinal equation: y−6=−11(x−6)y - 6 = -11(x - 6).

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