The equation is given as,
[tex]\begin{gathered} y\text{ = -}\frac{5}{2}x\text{ - 4} \\ \\ \\ \end{gathered}[/tex]Converting the given equation to standard form,
[tex]\begin{gathered} y\text{ = }\frac{-5x}{2}\text{ - }\frac{8}{2} \\ y\text{ = }\frac{-5x-8}{2} \\ 2y\text{ = -5x - 8} \\ 5x\text{ + 2y + 8 = 0} \end{gathered}[/tex]The slope of the given line is calculated as,
[tex]Slope\text{ = }\frac{-5}{2}[/tex]As the required line is parallel to the given line. Therefore slope of the required line is equal to the given line which is -5/2.
The required line passes through the point (5, -4).
The equation of a required line is calculated using the slope point formula.
[tex](y-y_1)\text{ = m}\times\text{\lparen x-x}_1)[/tex]Where,
[tex]\begin{gathered} m\text{ = }\frac{-5}{2} \\ (x_1,y_1)\text{ = \lparen 5, -4 \rparen} \end{gathered}[/tex]Required equation is calculated as,
[tex]\begin{gathered} (y-(-4))\text{ = }\frac{-5}{2}\text{ \lparen x- 5\rparen} \\ 2\times(y+4)\text{ = -5}\times\text{\lparen x - 5\rparen} \\ 2y\text{ + 8 = -5x + 25} \\ 5x\text{ + 2y + 8 - 25 = 0} \\ 5x\text{ + 2y -17 = 0} \end{gathered}[/tex]Thus the equation of the required line is,
[tex]5x\text{ + 2y - 17 = 0}[/tex]