We have the followed expression for a giving line:
[tex]2x+7y=5[/tex]Isolating the Y we find the expression:
[tex]y=\frac{-2}{7}x\text{ + }\frac{5}{7}[/tex]We know that if a line with expression y=mx+b is perpendicular to the line that the question gave to us, the product of the slopes of the two lines must be:
[tex]\frac{-2}{7}\times m=-1[/tex]With this last expression, we can find the slope for the line perpendicular to our first line:
[tex]\frac{-2}{7}\times m=-1\text{ }\Rightarrow\text{ m=}\frac{7}{2}[/tex]So, our slope is 7/2