Respuesta :
First, we need to clear y in the line given
[tex]\begin{gathered} 2x+9y=8 \\ 9y=-2x+8 \\ y=-\frac{2}{9}x+\frac{8}{9} \end{gathered}[/tex]because we need to have the slope-intercept form
[tex]y=mx+b[/tex]where m is the slope
if the line is parallel that have the same slope so the slope of the line that passes through (7,-5) is
m=-2/9
(7,-5)=(x1,y1)
In order to obtain the equation of the line
[tex]y-y_1=m(x-x_1)[/tex]then we substitute the values
[tex]\begin{gathered} y+5=-\frac{2}{9}(x-7) \\ y+5=-\frac{2}{9}x+\frac{14}{9} \\ y=-\frac{2}{9}x-\frac{31}{9} \end{gathered}[/tex]the equation of the line is
[tex]y=-\frac{2}{9}x-\frac{31}{9}[/tex]