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9-62. Find the equation of the line with slope -(3)/(5) passing through the point (-6,2).

Find the equation of the line with slope −35 -\frac{3}{5} passing through the point (−6,2) (-6,2) .

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Full solution

Q. Find the equation of the line with slope −35 -\frac{3}{5} passing through the point (−6,2) (-6,2) .
  1. Use Point-Slope Form: Use the point-slope form of the equation of a line, which is 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 the point through which the line passes.\newliney−2=−(35)(x+6)y - 2 = -\left(\frac{3}{5}\right)(x + 6)
  2. Distribute Slope: Distribute the slope −35-\frac{3}{5} across (x+6)(x + 6).\newliney - 22 = -\frac{33}{55}x - \left(\frac{33}{55}\right)\cdot 66
  3. Simplify Constant Term: Simplify the constant term.\newliney−2=−35x−185y - 2 = -\frac{3}{5}x - \frac{18}{5}
  4. Add 22 to Both Sides: Add 22 to both sides to get yy by itself.\newliney=−(35)x−185+2y = -\left(\frac{3}{5}\right)x - \frac{18}{5} + 2
  5. Convert 22 to Fraction: Convert 22 into a fraction with denominator 55 to combine with −185-\frac{18}{5}. \newliney=−(35)x−185+105y = -\left(\frac{3}{5}\right)x - \frac{18}{5} + \frac{10}{5}
  6. Combine Constant Terms: Combine the constant terms. y=−35x−85y = -\frac{3}{5}x - \frac{8}{5}

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