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What is the equation of the line that passes through the point (5,7) and has a slope of -(1)/(5) ? Answer:

What is the equation of the line that passes through the point (5,7) (5,7) and has a slope of −15 -\frac{1}{5} ?\newlineAnswer:

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Full solution

Q. What is the equation of the line that passes through the point (5,7) (5,7) and has a slope of −15 -\frac{1}{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.\newlineWe have:\newlineSlope mm: −15-\frac{1}{5}\newlinePoint (x1,y1)(x_1, y_1): (5,7)(5,7)\newlineThe slope-intercept form of a line is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
  2. Use point-slope form: Use the point-slope form of the equation of a line to find the y-intercept bb. The point-slope form is (y−y1)=m(x−x1)(y - y_1) = m(x - x_1). Substitute the given point and slope into the point-slope form: (y−7)=−15(x−5)(y - 7) = -\frac{1}{5}(x - 5)
  3. Simplify equation to find y: Simplify the equation to find the value of bb.
    (y−7)=−15x+15⋅5(y - 7) = -\frac{1}{5}x + \frac{1}{5}\cdot5
    (y−7)=−15x+1(y - 7) = -\frac{1}{5}x + 1
    Now, add 77 to both sides to solve for yy:
    y=−15x+1+7y = -\frac{1}{5}x + 1 + 7
    y=−15x+8y = -\frac{1}{5}x + 8

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