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What is the equation of the line that passes through the point (3,-5) and has a slope of -1 ? Answer:

What is the equation of the line that passes through the point (3,−5) (3,-5) and has a slope of −1-1 ?\newlineAnswer:

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Full solution

Q. What is the equation of the line that passes through the point (3,−5) (3,-5) and has a slope of −1-1 ?\newlineAnswer:
  1. Identify slope and point: Identify the slope and the point through which the line passes.\newlineWe are given the slope mm as −1-1 and the point (x1,y1)(x_1, y_1) as (3,−5)(3, -5).
  2. Use point-slope form: Use the point-slope form of the equation of a line to plug in the known values.\newlineThe point-slope form 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 the point the line passes through.
  3. Substitute values: Substitute the given slope and point into the point-slope form equation.\newline(y−(−5))=−1(x−3)(y - (-5)) = -1(x - 3)
  4. Simplify equation: Simplify the equation by distributing the slope and moving terms around to get the slope-intercept form, y=mx+by = mx + b.\newliney+5=−1(x−3)y + 5 = -1(x - 3)\newliney+5=−x+3y + 5 = -x + 3
  5. Isolate y: Isolate y to get the equation in slope-intercept form.\newliney=−x+3−5y = -x + 3 - 5\newliney=−x−2y = -x - 2

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