Determine the reduced equation of the straight line that is perpendicular to the straight line r: y=4x-10 and passes through the origin of the Cartesian plane

The line perpendicular to \(y = 4x - 10\) will have a slope that is the negative reciprocal of the slope of the given line \(y = 4x - 10\). The slope of \(y = 4x - 10\) is \(4\), so the perpendicular line will have a slope of \(-\frac{1}{4}\) (negative reciprocal). Given that the line passes through the origin \((0, 0)\), we can use the point-slope form of a line, \(y - y_1 = m(x - x_1)\), with the slope \(m = -\frac{1}{4}\) and the point \((x_1, y_1) = (0, 0)\). $4\[y - 0 = -\frac{1}{4}(x - 0)\]$$ \[y = -\frac{1}{4}x\] Therefore, the reduced equation of the straight line that is perpendicular to \(y = 4x - 10\) and passes through the origin is \(y = -\frac{1}{4}x\)