Answer:
y = 9
Step-by-step explanation:
Calculate the slope m of line k using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, 8) and (x₂, y₂ ) = (2, y)
m = [tex]\frac{y-8}{2-5}[/tex] = [tex]\frac{y-8}{-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]
The slope of line l is m = 3, thus slope of line k is
m = - [tex]\frac{1}{3}[/tex]
Equating the 2 slopes for line k
[tex]\frac{y-8}{-3}[/tex] = - [tex]\frac{1}{3}[/tex] ( multiply both sides by - 3 )
y - 8 = 1 ( add 8 to both sides )
y = 9
