the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 5x + 6y = 7 into this form
subtract 5x from both sides
6y = - 5x + 7 ( divide all terms by 6 )
y = - [tex]\frac{5}{6}[/tex] x + [tex]\frac{7}{6}[/tex] ← in slope-intercept form
with slope m = - [tex]\frac{5}{6}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex], hence
[tex]m_{perpendicular}[/tex] = - 1 / - [tex]\frac{5}{6}[/tex] = [tex]\frac{6}{5}[/tex]
y = [tex]\frac{6}{5}[/tex] x + c ← is the partial equation
to find c substitute (5, - 4 ) into the partial equation
- 4 = 6 + c ⇒ c = - 4 - 6 = - 10
y = [tex]\frac{6}{5}[/tex] x - 10 ← equation in slope-intercept form
