Answer:
y = [tex]\frac{3}{2}[/tex] x + 8
Step-by-step explanation:
the equation of a line in slope intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 2x + 3y = 9 into this form
subtract 2x from both sides
3y = - 2x + 9 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + 3 ← in slope-intercept form
with slope m = - [tex]\frac{2}{3}[/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] = -[tex]\frac{1}{-2/3}[/tex] = [tex]\frac{3}{2}[/tex], hence
y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute (- 2, 5) into the partial equation
5 = - 3 + c ⇒ c = 5 + 3 = 8
y = [tex]\frac{3}{2}[/tex] x + 8 ← equation of perpendicular line
