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The equation of line vv is y=9x+1y = 9x + 1. Line ww is perpendicular to line vv and passes through (3,2)(3,-2). What is the equation of line ww?\newlineWrite the equation in slope-intercept form.

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Q. The equation of line vv is y=9x+1y = 9x + 1. Line ww is perpendicular to line vv and passes through (3,2)(3,-2). What is the equation of line ww?\newlineWrite the equation in slope-intercept form.
  1. Perpendicular Lines Slopes: Line ww is perpendicular to line vv.\ Are their slopes the same or opposite reciprocals?\ Slopes of perpendicular lines are opposite reciprocals.
  2. Equation of Line v: Equation of line v: \newliney=9x+1y = 9x + 1\newlineFind the slope of line v.\newlineCompare y=9x+1y = 9x + 1 with y=mx+by = mx + b.\newlinem=9m = 9\newlineSlope of line v: 99
  3. Slope of Line ww: Line ww is perpendicular to vv.\newlineSlope of line vv: 99\newlineFind the slope of line ww.\newlineOpposite reciprocal of 99 is 19-\frac{1}{9}.\newlineSlope of line ww: 19-\frac{1}{9}
  4. Finding Y-Intercept: For line ww: \newlineSlope (mm): 19-\frac{1}{9}\newlinePoint: (3,2)(3, -2)\newlinePlug these values in y=mx+by = mx + b and find the y-intercept.\newline2=19(3)+b-2 = -\frac{1}{9}(3) + b\newline2=13+b-2 = -\frac{1}{3} + b\newline2+13=b-2 + \frac{1}{3} = b\newline63+13=b-\frac{6}{3} + \frac{1}{3} = b\newline53=b-\frac{5}{3} = b
  5. Equation of Line w: For line w: \newlineSlope mm: 19-\frac{1}{9}\newliney-intercept bb: 53-\frac{5}{3}\newlineWhat is the equation of the line w in slope-intercept form?\newlineSubstitute 19-\frac{1}{9} for mm and 53-\frac{5}{3} for bb in y=mx+by = mx + b.\newliney=19x53y = -\frac{1}{9}x - \frac{5}{3}

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