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Use point-slope form to write the equation of a line that passes through the point (-7,-8) with slope -(2)/(5). Answer:

Use point-slope form to write the equation of a line that passes through the point (−7,−8) (-7,-8) with slope −25 -\frac{2}{5} .\newlineAnswer:

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Full solution

Q. Use point-slope form to write the equation of a line that passes through the point (−7,−8) (-7,-8) with slope −25 -\frac{2}{5} .\newlineAnswer:
  1. 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.
  2. Given Slope and Point: Given the slope m=−25m = -\frac{2}{5} and the point (−7,−8)(-7, -8), we can substitute these values into the point-slope form equation.
  3. Substitute Values: Substituting the given point and slope into the point-slope form, we get:\newline(y−(−8))=−25(x−(−7))(y - (-8)) = -\frac{2}{5}(x - (-7))
  4. Simplify Equation: Simplify the equation by distributing the slope and removing the double negatives:\newline(y+8)=−(25)(x+7)(y + 8) = -\left(\frac{2}{5}\right)(x + 7)
  5. Final 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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