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

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Answer to a math question 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

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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 $y = -\frac{1}{4}x$

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