perpendicular slope = [tex]\frac{5}{4}[/tex]
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 4x + 5y = 2 into this form
subtract 4x from both sides
5y = - 4x + 2 ( divide all terms by 5 )
y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{2}{5}[/tex] ← in slope-intercept form
with slope m = - [tex]\frac{4}{5}[/tex]
given the slope m of a line then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - 1 /- [tex]\frac{4}{5}[/tex] = [tex]\frac{5}{4}[/tex]
