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Geometry \newline> E. 55 Equations of parallel and perpendicular lines VEB\newlineVideo (D)\newlineQuestions\newlineanswered\newlineThe equation for line \newlinev can be written as \newliney=−97x−5y=-\frac{9}{7}x-5. Line \newlinew, which is perpendicular to line \newlinev, includes the point \newline(9,6)(9,6). What is the equation of line \newlinew ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.\newlineSubmit\newline501501\newlineTime\newlineelapsed\newline\newline0606\newline0000\newline2222\newline\newlineHR\newlineMIN\newlineSEC\newline\newlineSmartscore\newlineout of 100100 ?\newline2222\newlinei11.\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSlopes of parallel and perpendicular lines (8383) \newlineN\newlineEquations of lines (2626)\newlineLesson: Equations of parallel and perpendicular lines

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Q. Geometry \newline> E. 55 Equations of parallel and perpendicular lines VEB\newlineVideo (D)\newlineQuestions\newlineanswered\newlineThe equation for line \newlinev can be written as \newliney=−97x−5y=-\frac{9}{7}x-5. Line \newlinew, which is perpendicular to line \newlinev, includes the point \newline(9,6)(9,6). What is the equation of line \newlinew ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.\newlineSubmit\newline501501\newlineTime\newlineelapsed\newline\newline0606\newline0000\newline2222\newline\newlineHR\newlineMIN\newlineSEC\newline\newlineSmartscore\newlineout of 100100 ?\newline2222\newlinei11.\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSlopes of parallel and perpendicular lines (8383) \newlineN\newlineEquations of lines (2626)\newlineLesson: Equations of parallel and perpendicular lines
  1. Identify slope of line vv: Identify the slope of line vv. The equation of line vv is given as y=−(97)x−5y = -\left(\frac{9}{7}\right)x - 5. The slope of line vv is the coefficient of xx, which is −(97)-\left(\frac{9}{7}\right).
  2. Determine slope of line ww: Determine the slope of line ww. Since line ww is perpendicular to line vv, its slope will be the negative reciprocal of the slope of line vv. The negative reciprocal of −(97)-\left(\frac{9}{7}\right) is 79\frac{7}{9}.
  3. Use point-slope form: Use the point-slope form to write the equation of line ww. 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 know that line ww passes through the point (9,6)(9,6) and has a slope of 79\frac{7}{9}.
  4. Substitute slope and point: Substitute the slope and point into the point-slope form.\newlineUsing the point (9,6)(9,6) and the slope 79\frac{7}{9}, the equation becomes y−6=(79)(x−9)y - 6 = \left(\frac{7}{9}\right)(x - 9).
  5. Simplify to slope-intercept form: Simplify the equation to slope-intercept form.\newlineTo get the equation into slope-intercept form y=mx+by = mx + b, we distribute the slope and add 66 to both sides:\newliney−6=(79)x−(79)⋅9y - 6 = \left(\frac{7}{9}\right)x - \left(\frac{7}{9}\right)\cdot 9\newliney−6=(79)x−7y - 6 = \left(\frac{7}{9}\right)x - 7\newliney=(79)x−7+6y = \left(\frac{7}{9}\right)x - 7 + 6\newliney=(79)x−1y = \left(\frac{7}{9}\right)x - 1

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