write the equation of the line that passes through the point (6,2) and is perpendicular to a line that passes through the points (-5,3) and (-1,-9

                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):

The slope of a line perpendicular to the line with the slope m₀:

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