Answer:
see explanation
Step-by-step explanation:
(a ) calculate the slope m using the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = A(0, 6) and (x₂, y₂ ) = B(3, 0 )
[tex]m_{AB}[/tex] = [tex]\frac{0-6}{3-0}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2
(b)
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}[/tex] = [tex]\frac{1}{2}[/tex]
(c)
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
(0, 6 ) is the y-intercept ⇒ c = 6
y = [tex]\frac{1}{2}[/tex] x + 6 ← equation of perpendicular line
