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Use point-slope form to write the equation of a line that passes through the point (-12,16) with slope (15)/(8). Answer:

Use point-slope form to write the equation of a line that passes through the point (−12,16) (-12,16) with slope 158 \frac{15}{8} .\newlineAnswer:

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Full solution

Q. Use point-slope form to write the equation of a line that passes through the point (−12,16) (-12,16) with slope 158 \frac{15}{8} .\newlineAnswer:
  1. Point-Slope Form Equation: The point-slope form of the equation of a line is given by (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.
  2. Substitute Values: Given the point (−12,16)(-12, 16) and the slope 158\frac{15}{8}, we can substitute these values into the point-slope form equation.
  3. Simplify Equation: Substituting the given point and slope into the equation, we get (y−16)=(158)(x−(−12))(y - 16) = \left(\frac{15}{8}\right)(x - (-12)).
  4. Final Answer: Simplify the equation by distributing the slope and removing the double negative in the xx term: (y−16)=(158)(x+12)(y - 16) = \left(\frac{15}{8}\right)(x + 12).
  5. Final Answer: Simplify the equation by distributing the slope and removing the double negative in the xx term: (y−16)=(158)(x+12)(y - 16) = \left(\frac{15}{8}\right)(x + 12).The equation in point-slope form is now (y−16)=(158)(x+12)(y - 16) = \left(\frac{15}{8}\right)(x + 12). This is the final answer.

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