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Line tt has an equation of y=10x8y = 10x - 8. Line uu is perpendicular to line tt and passes through (10,6)(-10,-6). What is the equation of line uu?\newlineWrite the equation in slope-intercept form.

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Q. Line tt has an equation of y=10x8y = 10x - 8. Line uu is perpendicular to line tt and passes through (10,6)(-10,-6). What is the equation of line uu?\newlineWrite the equation in slope-intercept form.
  1. Perpendicular Lines Slopes: Line uu is perpendicular to line tt.\newlineAre their slopes the same or opposite reciprocals?\newlineSlopes of perpendicular lines are opposite reciprocals.
  2. Equation of Line t: Equation of line t: \newliney=10x8y = 10x - 8\newlineFind the slope of line t.\newlineCompare y=10x8y = 10x - 8 with y=mx+by = mx + b.\newlinem=10m = 10\newlineSlope of line t: 1010
  3. Slope of Line uu: Line uu is perpendicular to line tt.\newlineSlope of line tt: 1010\newlineFind the slope of line uu.\newlineOpposite reciprocal of 1010 is 110-\frac{1}{10}.\newlineSlope of line uu: 110-\frac{1}{10}
  4. Finding Y-Intercept: For line uu: \newlineSlope (mm): 110-\frac{1}{10}\newlinePoint: (10,6)(-10, -6)\newlinePlug these values in y=mx+by = mx + b and find the y-intercept.\newline6=110(10)+b-6 = -\frac{1}{10}(-10) + b\newline6=1+b-6 = 1 + b\newline7=b-7 = b
  5. Equation of Line u: For line u: \newlineSlope mm: 110-\frac{1}{10}\newliney-intercept bb: 7-7\newlineWhat is the equation of the line u in slope-intercept form?\newlineSubstitute 110-\frac{1}{10} for mm and 7-7 for bb in y=mx+by = mx + b.\newliney=110x7y = -\frac{1}{10}x - 7

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