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Write the equation of the line that passes through the points (1,9) and (-3,2). 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 (1,9) (1,9) and (−3,2) (-3,2) . 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 (1,9) (1,9) and (−3,2) (-3,2) . 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} with the given points (1,9)(1,9) and (−3,2)(-3,2).\newlinem=2−9−3−1m = \frac{2 - 9}{-3 - 1}\newlinem=−7−4m = \frac{-7}{-4}\newlinem=74m = \frac{7}{4}
  2. Choose point: Choose one of the points to use in the point-slope form equation. We can use either (1,9)(1,9) or (−3,2)(-3,2). Let's use (1,9)(1,9).
  3. Write equation: Write the equation of the line in point-slope form using the slope m=74m = \frac{7}{4} and the point (1,9)(1,9). The point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1).\newlineSubstitute m=74m = \frac{7}{4} and the point (1,9)(1,9) into the equation:\newliney−9=(74)(x−1)y - 9 = \left(\frac{7}{4}\right)(x - 1)
  4. Check simplification: Check the equation to ensure it is fully simplified and in the correct form. The equation y−9=74(x−1)y - 9 = \frac{7}{4}(x - 1) is already in the simplest point-slope form.

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