Answer
Point-Slope form: $y - 5 = 4(x + 2)$
Slope-Intercept form: $y = 4x + 13$
General form: $4x - y + 13 = 0$
Work Step by Step
The product of the slopes of perpendicular lines results in -1. Therefore, to find the missing linear equation, we use the slope of the equation given and solve as follows: $$-1 = -\frac{1}{4}m_{perp}$$ $$4 = m_{perp}$$ The easiest way to find the equation is to now use point-slope form with the point given: $$y - 5 = 4(x - (-2))$$ $$y -5 = 4(x + 2)$$ From here, we can derive both the slope-intercept form: $$y - 5 = 4(x + 2)$$ $$y - 5 = 4x + 8$$ $$y = 4x + 8 + 5$$ $$y = 4x + 13$$ and by passing the $y$ to the other side, we can arrive at the general form: $$y = 4x + 13$$ $$0 = 4x - y + 13$$
