Recall that given the slope, m₁, of the equation of the line, we can find the slope, m₂, of the line perpendicular to it is equal to the negative reciprocal of m₁.
Given that the equation is equal to y = (-1/2)x + 4, slope is equal to -1/2. The negative reciprocal of the slope would be 2. That would be m₂ = 2. Now, since the point (-2, 4) passes through this line, we can use the point-slope form of the line shown below.
(y - y₁) = m(x - x₁)
where (x₁, y₁) for this case is (-2, 4) and m = 2. So, we now have
(y - 4) = 2(x - (-2))
y - 4 = 2x + 8
y = 2x +12
Thus, the equation of the line is y = 2x + 12.
Answer: 2x + 12
