Answer:
y = [tex]\frac{4}{3}[/tex] x
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 )
y = - [tex]\frac{3}{4}[/tex] x + 1 ← is in slope- intercept form
with slope m = - [tex]\frac{3}{4}[/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}{-\frac{3}{4} }[/tex] = [tex]\frac{4}{3}[/tex] , thus
y = [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute (9, 12) into the partial equation
12 = 12 + c ⇒ c = 12 - 12 = 0
y = [tex]\frac{4}{3}[/tex] x + 0 , which simplifies to
y = [tex]\frac{4}{3}[/tex] x