Question

Write an equation of a line in slope intercept form that is perpendicular to the line 2x -3y = 12 and passes through the point (2, 6).

Answer 1

  2x - 3y = 12
- 2x         - 2x
        -3y = -2x + 12
         -3          -3
           y = ²/₃x - 4

y - y₁ = m(x - x₁)
 y - 6 = -1¹/₂(x - 2)
 y - 6 = -1¹/₂(x) + 1¹/₂(2)
 y - 6 = -1¹/₂x + 3
   + 6             + 6
      y = -1¹/₂x + 9

Answer 2

a perpendicular line has a slope equal to the negative reciprocal of the original slope. In this case, the perpendicular line's slope is equal to -1/2. we use the slope intercept general form of y-y1 = m *(x-x1) in which upon substitution, the form becomes y - 6 = -1/2 * ( x-2) ; y = -1/2x + 7