Find the equation of the line through the given point and perpendicular to the given line.

Point: (0, 0)

Line: \(-2x + 4y = 12\)

-2x+4y=12 <=> y = (-1/2)x + 3 => the slope of given line is -1/2;
the new line and the given line are perpendicular =>( the slope of new line )*(-1/2) = -1 =>
the slope of new line is 2;
the equation of the new line is y -0 =2( x -0) <=> y = 2x.

Answered by crisforp | 2024-06-10

-2x+0 is perpendicular to -2x+4y=12, and go through (0,0). So the answer is -2x+0

Answered by jennyjjjj | 2024-06-10

The equation of the line that is perpendicular to the given line and passes through the point (0, 0) is y = − 2 x . This is derived from finding the slope of the original line, determining the perpendicular slope, and applying the point-slope form of a line. The original line has a slope of 2 1 ​ , leading to a perpendicular slope of − 2 .
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Answered by crisforp | 2024-12-23