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Use point-slope form to write the equation of a line that passes through the point (-5,-12) with slope (9)/(5). Answer:

Use point-slope form to write the equation of a line that passes through the point (−5,−12) (-5,-12) with slope 95 \frac{9}{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 (−5,−12) (-5,-12) with slope 95 \frac{9}{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. Substitute Values: Given the point (−5,−12)(-5, -12) and the slope 95\frac{9}{5}, we can substitute these values into the point-slope form equation.\newline(y−(−12))=(95)(x−(−5))(y - (-12)) = \left(\frac{9}{5}\right)(x - (-5))
  3. Simplify Equation: Simplify the equation by distributing the slope and removing the double negatives.\newline(y+12)=(95)(x+5)(y + 12) = \left(\frac{9}{5}\right)(x + 5)
  4. Final Equation: The equation is now in point-slope form and there is no need to simplify further unless asked to convert to another form.

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