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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]