Answer:
see the explanation
Step-by-step explanation:
we have
[tex]5y=2x+4[/tex]
Solve for y
[tex]y=\frac{2}{5}x+\frac{4}{5}[/tex]
This is the equation of the line in slope intercept form
The slope m of the given equation is
[tex]m=\frac{2}{5}[/tex]
we know that
If two lines are perpendicular,, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
so
Find the slope of the line perpendicular to the given line
[tex]m1*m2=-1[/tex]
we have
[tex]m1=\frac{2}{5}[/tex]
substitute
[tex](\frac{2}{5})*m2=-1[/tex]
[tex]m2=-\frac{5}{2}=-2.5[/tex]
therefore
All equations of the line having as slope [tex]m=-2.5[/tex] will be perpendicular to the given line.
