Answered

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Write and equation in slope intercept form for the line that is perpendicular to the line you graphed using y=-5/2x-3 and passing through points (-5,2)

Sagot :

devishri1977

Answer:

[tex]\sf y =\dfrac{2}{5}x+4[/tex]

Step-by-step explanation:

 [tex]\sf y = \dfrac{-5}{2}x-3\\\\\\m_1=\dfrac{-5}{2}[/tex]

[tex]\sf \text{Slope of the perpendicular line = $\dfrac{-1}{m_1}$}[/tex]

                                                 [tex]\sf m =\dfrac{-1}{\dfrac{-5}{2}}\\\\\\= -1*\dfrac{-2}{5}\\\\= \dfrac{2}{5}[/tex]

[tex]\sf slope = m = \dfrac{2}{5}[/tex]  

Line passes thorugh ( -5 , 2)

Equation of line:  y = mx + b

         [tex]\sf y = \dfrac{2}{5}x + b[/tex]

Substitute the point(-5,2) in the above equation and find the value of 'b'.

          [tex]\sf 2 =\dfrac{2}{5}*(-5)+b\\\\\\ 2 = -2 + b\\[/tex]

     2+ 2 = b

           b = 4

  Equation of the line :

              [tex]\sf \boxed{y =\dfrac{2}{5}x+4}[/tex]

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