Answer:
y - 2 = ¹/₃(x - 6) ← the point-slope form of the equation
y = ¹/₃x ← the slope-intercept form of the equation
x - 3y = 0 ← standard form of the equation
Step-by-step explanation:
The slope of line that passes through (-5, 3) and (-1, -9):
[tex]m_0=\dfrac{3-(-9)}{-5-(-1)}=\dfrac{3+9}{-5+1}=\dfrac{12}{-4}=-3[/tex]
The slope of a line perpendicular to the line with the slope m₀:
[tex]m=-\dfrac1{m_0}=-\dfrac1{-3}=\dfrac13[/tex]
The point-slope form of the equation of a line: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passing through.
(6, 2) ⇒ x₁ = 6, y₁ = 2
So:
y - 2 = ¹/₃(x - 6) ← the point-slope form of the equation
y - 2 = ¹/₃x - 2 {add 2 to both sides}
y = ¹/₃x ← the slope-intercept form of the equation
y - ¹/₃x = 0 {multiply both sides by (-3)}
x - 3y = 0 ← standard form of the equation
