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Use point-slope form to write the equation of a line that passes through the point (-5,3) with slope -(1)/(3). Answer:

Use point-slope form to write the equation of a line that passes through the point (−5,3) (-5,3) with slope −13 -\frac{1}{3} .\newlineAnswer:

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Q. Use point-slope form to write the equation of a line that passes through the point (−5,3) (-5,3) with slope −13 -\frac{1}{3} .\newlineAnswer:
  1. Recall Point-Slope Form: Recall the point-slope form of a line's equation. 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. Identify Slope and Point: Identify the slope mm and the point (x1,y1)(x_1, y_1) given in the problem.\newlineThe slope mm is given as −13-\frac{1}{3}, and the point (x1,y1)(x_1, y_1) is given as (−5,3)(-5, 3).
  3. Substitute Values: Substitute the slope and the point into the point-slope form equation.\newlineUsing the slope m=−13m = -\frac{1}{3} and the point (x1,y1)=(−5,3)(x_1, y_1) = (-5, 3), we substitute these values into the point-slope form equation:\newline(y−3)=−13(x−(−5))(y - 3) = -\frac{1}{3}(x - (-5))
  4. Simplify Equation: Simplify the equation by distributing the slope on the right-hand side.\newline(y−3)=−13(x+5)(y - 3) = -\frac{1}{3}(x + 5)
  5. Check for Simplification: Check the equation for any possible simplification.\newlineThe equation (y−3)=−13(x+5)(y - 3) = -\frac{1}{3}(x + 5) is already in the simplest form and correctly represents the point-slope form of the line.

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