Respuesta :
Answer:
see explanation
Step-by-step explanation:
We require to find the slope m of the line joining the 2 given points
To find m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2,3) and (x₂, y₂ ) = (1, - 2)
m = [tex]\frac{-2-3}{1-2}[/tex] = [tex]\frac{-5}{-1}[/tex] = 5
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}{5}[/tex]
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept ), thus
y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the perpendicular line
To find c substitute (- 3, 2) into the partial equation
2 = [tex]\frac{3}{5}[/tex] + c ⇒ c = [tex]\frac{7}{5}[/tex]
y = - [tex]\frac{1}{5}[/tex] x + [tex]\frac{7}{5}[/tex] ← perpendicular equation
