Answer:
y = [tex]\frac{5}{4}[/tex] x + 7
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{4}{5}[/tex] x + 3 is in this form
with m = - [tex]\frac{4}{5}[/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{4}{5} }[/tex] = [tex]\frac{5}{4}[/tex], hence
y = [tex]\frac{5}{4}[/tex] x + c ← is the partial equation
To find c substitute (4, 12) into the partial equation
12 = 5 + c ⇒ c = 12 - 5 = 7
y = [tex]\frac{5}{4}[/tex] x + 7 ← equation of perpendicular line
