Question

the line equation that goes through (3,4) and perpendicular to y=-2

Answer 1

A line perpendicular to y = -2 would have to start with x = some number

And this perpendicular line has to go through the point (3,4). And 3 is the x-value so the line that goes through (3,4) and is pependicular to y = -2 is x = 3.

Your answer is x = 3.

Answer 2

y - y₁ = m(x - x₁)
y - 4 = ¹/₂(x - 3)
y - 4 = ¹/₂(x) - ¹/₂(3)
y - 4 = ¹/₂x - 1¹/₂
  + 4          + 4
     y = ¹/₂x + 2¹/₂