Answer
$$y = 4x + 22$$
Work Step by Step
For two lines to intersect perpendicular to each other on a coordinate plane, the product of their slopes must equal -1. The equation given describes a line with slope $m = -\frac{1}{4}$. To find the equation of the other line, we must first solve for its slope: $$-1 = -\frac{1}{4}m_{perpendicular}$$ $$4 = m_{perpendicular}$$ Using the point $(-4, 6)$, we can write the line's equation in slope-intercept form: $$y-6 = 4(x + 4)$$ $$y - 6 = 4x + 16$$ $$y = 4x + 16 + 6$$ $$y = 4x + 22$$
