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Use point-slope form to write the equation of a line that passes through the point (-5,14) with slope -(5)/(3). Answer:

Use point-slope form to write the equation of a line that passes through the point (−5,14) (-5,14) with slope −53 -\frac{5}{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 (−5,14) (-5,14) with slope −53 -\frac{5}{3} .\newlineAnswer:
  1. Point-Slope Form Definition: 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.
  2. Substitute Given Values: Given the point (−5,14)(-5, 14) and the slope −53-\frac{5}{3}, 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−14)=−53(x−(−5))(y - 14) = -\frac{5}{3}(x - (-5)).
  4. Final Point-Slope Form: Simplify the equation by distributing the slope and removing the double negative in front of the 55: (y−14)=−(53)(x+5)(y - 14) = -\left(\frac{5}{3}\right)(x + 5).
  5. Final Point-Slope Form: Simplify the equation by distributing the slope and removing the double negative in front of the 55: (y−14)=−53(x+5)(y - 14) = -\frac{5}{3}(x + 5).The equation of the line in point-slope form is now (y−14)=−53(x+5)(y - 14) = -\frac{5}{3}(x + 5). This is the final simplified form.

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