Respuesta :

anbu40

Answer:

k = 12

Step-by-step explanation:

  • Write the equation of line L in slope-intercept form: y = mx +b.

          4y - 6x = 33

                 4y = 6x + 33

                   [tex]\sf y = \dfrac{6}{4}x+\dfrac{33}{4}\\\\\\y=\dfrac{3}{2}x+\dfrac{33}{4}[/tex]

[tex]\sf Slope = \dfrac{3}{2}[/tex]

  • The product of slope of perpendicular line is (-1). So, the slope of line M will the negative reciprocal of the slope of line L.

 [tex]\sf Slope \ of \ the \ line \ M = \dfrac{-2}{3}[/tex]

   Equation of line M:

                     [tex]\sf y =\dfrac{-2}{3}x + b[/tex]

  • Line M passes through the point A(5,6).  We can find the y-intercept of line M by substituting the x and y value in the above equation.

                [tex]\sf 6 = \dfrac{-2}{3}*5+b\\\\\\ 6 = \dfrac{-10}{3}+b\\\\\\ b = 6 + \dfrac{10}{3}\\\\\\b = \dfrac{6*3}{1*3}+\dfrac{10}{3}\\\\\\b = \dfrac{18+10}{3}\\\\b = \dfrac{28}{3}[/tex]

  • Equation of line M:

                 [tex]\sf y =\dfrac{-2}{3}x+\dfrac{28}{3}[/tex]

  • Point B(-4, k) passes through line M. We can find k, by substituting the x and y value in the above equation.

                 [tex]\sf k = \dfrac{-2}{3}*(-4)+\dfrac{28}{3}\\\\\\k = \dfrac{8+28}{3}\\\\\\k =\dfrac{36}{3}\\\\\boxed{\bf k = 12}[/tex]

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