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ad the equation of the line perpendicular to y=9 through the point (-6,-2)

ad the equation of the line perpendicular to y=9 y=9 through the point (−6,−2) (-6,-2)

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Full solution

Q. ad the equation of the line perpendicular to y=9 y=9 through the point (−6,−2) (-6,-2)
  1. Find Slope of Line: Find the slope of the line y=9y=9. Since it's a horizontal line, the slope is 00.
  2. Perpendicular Line Slope: Determine the slope of the line perpendicular to y=9y=9. Perpendicular lines have slopes that are negative reciprocals. The negative reciprocal of 00 is undefined, which means the perpendicular line is vertical.
  3. Vertical Line Equation: Write the equation of the vertical line passing through (−6,−2)(-6,-2).\newlineA vertical line has the form x=ax=a, where aa is the xx-coordinate of the point it passes through.
  4. Substitute X-coordinate: Substitute the xx-coordinate of the point into the equation.x=−6x=-6 is the equation of the vertical line.
  5. Check Point on Line: Check if the line passes through the given point (−6,−2)(-6,-2).\newlineSubstitute −6-6 for xx and see if the yy-coordinate is −2-2.\newlineSince it's a vertical line, all points on the line have x=−6x=-6, so it passes through (−6,−2)(-6,-2).

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