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What is the equation of a line passing through the coodinates of 3 -4 and is perpendicular to the line 5x-2y equals 3?
Wiki User
∙ 11y ago
It works out as: 2x+5y+14 = 0 in its general form.
Recall that the slopes of perpendicular lines are negative reciprocals.
So let's find the slope of the line with equation 5x - 2y = 3.
5x - 2y = 3 subtract 5x to both sides
-2y = -5x + 3 divide each term of the both sides by -2
y = (5/2)x - 3/2
Thus, the slope of the perpendicular line is 5/2.
The slope of our line is the negative reciprocal of 5/2. It is therefore -2/5.
Using the point-slope form, we have the equation
y - (-4) = -2/5(x - 3)
y + 4 = -(2/5)x + 6/5 subtract 4 to both sides
y = -(2/5)x - 14/5 (the slope-intercept form)
Wiki User
∙ 11y ago
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