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IX. IXL - Equations of parallel an\newline←→ \leftarrow \rightarrow C \newline−@(@−@) \quad-@^(@-@) ixl.com/math/geometry/equations-of-parallel-and-perpendicular-lines\newline77th Grade Science...\newlineMicrosoft Forms\newline(144144) Hot Wheels...\newlineCuEs\newline宜家VIMLE 维姆勒.. \text{宜家VIMLE 维姆勒}.. \newlineQuizizz Creator\newlineNew Tab\newlineGeoGebra - the w...\newlineResearch for Scien...\newlineGeometry - GeoG..\newlineAll Bookmarks\newlineMy IXL Learning Assessment Analytics\newlineGeometry \newline> E. 55 Equations of parallel and perpendicular lines VEB\newlineVideo (D \text{D} )\newlineQuestions\newlineThe equation for line \newliner r can be written as \newliney=12x+8 y=\frac{1}{2}x+8 . Line \newlines s , which is perpendicular to line \newliner r , includes the point \newline(2,−7) (2,-7) . What is the equation of line \newlines s ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.\newlineSubmit\newline−@(@−@) \quad-@^(@-@) 00\newlineSubmit\newline−@(@−@) \quad-@^(@-@) 11\newline−@(@−@) \quad-@^(@-@) 22\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSlopes of parallel and perpendicular lines (−@(@−@) \quad-@^(@-@) 33) \newlineI\newlineEquations of lines (−@(@−@) \quad-@^(@-@) 44)\newlineLesson: Equations of parallel and perpendicular lines

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Q. IX. IXL - Equations of parallel an\newline←→ \leftarrow \rightarrow C \newline−@(@−@) \quad-@^(@-@) ixl.com/math/geometry/equations-of-parallel-and-perpendicular-lines\newline77th Grade Science...\newlineMicrosoft Forms\newline(144144) Hot Wheels...\newlineCuEs\newline宜家VIMLE 维姆勒.. \text{宜家VIMLE 维姆勒}.. \newlineQuizizz Creator\newlineNew Tab\newlineGeoGebra - the w...\newlineResearch for Scien...\newlineGeometry - GeoG..\newlineAll Bookmarks\newlineMy IXL Learning Assessment Analytics\newlineGeometry \newline> E. 55 Equations of parallel and perpendicular lines VEB\newlineVideo (D \text{D} )\newlineQuestions\newlineThe equation for line \newliner r can be written as \newliney=12x+8 y=\frac{1}{2}x+8 . Line \newlines s , which is perpendicular to line \newliner r , includes the point \newline(2,−7) (2,-7) . What is the equation of line \newlines s ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.\newlineSubmit\newline−@(@−@) \quad-@^(@-@) 00\newlineSubmit\newline−@(@−@) \quad-@^(@-@) 11\newline−@(@−@) \quad-@^(@-@) 22\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSlopes of parallel and perpendicular lines (−@(@−@) \quad-@^(@-@) 33) \newlineI\newlineEquations of lines (−@(@−@) \quad-@^(@-@) 44)\newlineLesson: Equations of parallel and perpendicular lines
  1. Identify slope of line r: Identify the slope of line r.\newlineThe equation of line r is given as y=(12)x+8y = (\frac{1}{2})x + 8. The slope of line r is the coefficient of xx, which is 12\frac{1}{2}.
  2. Determine slope of line ss: Determine the slope of line ss.\newlineSince line ss is perpendicular to line rr, its slope will be the negative reciprocal of the slope of line rr. The negative reciprocal of 12\frac{1}{2} is −2-2.
  3. Use point-slope form: Use the point-slope form to write the equation of line ss. The point-slope form of a line is 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 a point on the line. We have the slope of line ss as −2-2 and the point (2,−7)(2, -7).
  4. Substitute slope and point: Substitute the slope and point into the point-slope form.\newlineUsing the point (2,−7)(2, -7) and the slope −2-2, the equation becomes y−(−7)=−2(x−2)y - (-7) = -2(x - 2).
  5. Simplify to slope-intercept form: Simplify the equation to slope-intercept form.\newlineFirst, distribute the −2-2: y+7=−2x+4y + 7 = -2x + 4.\newlineNext, subtract 77 from both sides to isolate yy: y=−2x+4−7y = -2x + 4 - 7.\newlineFinally, combine like terms: y=−2x−3y = -2x - 3.

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