What is the equation of the line passing through the point (-2, 4) and perpendicular to y = -one halfx + 4?

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. 2x + 12