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Use point-slope form to write the equation of a line that passes through the point (-14,-7) with slope (2)/(3). Answer:

Use point-slope form to write the equation of a line that passes through the point (−14,−7) (-14,-7) with slope 23 \frac{2}{3} .\newlineAnswer:

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Full solution

Q. Use point-slope form to write the equation of a line that passes through the point (−14,−7) (-14,-7) with slope 23 \frac{2}{3} .\newlineAnswer:
  1. Identify Point-Slope Form: The point-slope form of a line's equation 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.\newlineGiven the point (−14,−7)(-14, -7) and the slope 23\frac{2}{3}, we can substitute these values into the point-slope form equation.
  2. Substitute Values: Substitute the given point and slope into the point-slope form equation:\newline(y−(−7))=(23)(x−(−14))(y - (-7)) = \left(\frac{2}{3}\right)(x - (-14))
  3. Simplify Equation: Simplify the equation by distributing the slope and removing the double negative signs:\newline(y+7)=(23)(x+14)(y + 7) = \left(\frac{2}{3}\right)(x + 14)
  4. Finalize Equation: The equation is now in point-slope form and there is no need for further simplification unless asked to convert it to another form.

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