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What is the equation of the line that passes through the point (5,-5) and has a slope of -(3)/(5) ? Answer:

What is the equation of the line that passes through the point (5,−5) (5,-5) and has a slope of −35 -\frac{3}{5} ?\newlineAnswer:

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Full solution

Q. What is the equation of the line that passes through the point (5,−5) (5,-5) and has a slope of −35 -\frac{3}{5} ?\newlineAnswer:
  1. Identify slope and point: Identify the slope mm and the point (x1,y1)(x_1, y_1) through which the line passes.\newlineThe slope is given as m=−35m = -\frac{3}{5}, and the point is (5,−5)(5, -5).
  2. Use point-slope form: Use the point-slope form of the equation of a line to plug in the values.\newlineThe point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1).\newlineHere, y1=−5y_1 = -5, x1=5x_1 = 5, and m=−35m = -\frac{3}{5}.\newlineSo, y−(−5)=−35(x−5)y - (-5) = -\frac{3}{5}(x - 5).
  3. Simplify equation: Simplify the equation to get it into slope-intercept form y=mx+by = mx + b.y+5=−35x+35×5y + 5 = -\frac{3}{5}x + \frac{3}{5} \times 5y+5=−35x+3y + 5 = -\frac{3}{5}x + 3
  4. Subtract to solve for y: Subtract 55 from both sides to solve for y.\newliney=−35x+3−5y = -\frac{3}{5}x + 3 - 5\newliney=−35x−2y = -\frac{3}{5}x - 2

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