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Slope of a line perpendicular to x-y=16
Line B is perpendicular to Line A if its slope is the negative reciprocal of the slope of Line A.When a linear equation is in the formy = mx + b,m is the slope, and b is the y-intercept. So, for example,y = (2/3)x + 5is perpendicular toy = (-3/2)x + 7.(The y-intercepts in these two equations are random numbers.)
7x + 10y = 4.5 : 10y = -7x + 4.5 : y = -x.7/10 + 0.45, the gradient of this line is -7/10 Two straight lines are perpendicular if the product of their gradients is -1. Let the equation for the perpendicular line be y = mx + c Then m x -7/10 = -1 : m = 10/7 The equation for the perpendicular line is y = x.10/7 + c If the values of x and y for the point of intersection are provided then these can be substituted in the perpendicular line equation and the value of c obtained. If appropriate, the equation can then be restructured to a format similar to the original equation.
If the gradient of a line is m, the gradient of a line perpendicular to it (m') is such that mm' = -1, that is: m' = -1/m So for: y = -x - 5 m = -1, so the gradient of a perpendicular line is: m' = -1/-1 = 1 So a general line perpendicular to y = -x - 5 would be: y = x + c A specific line perpendicular to y = -x - 5 at point (xo, -xo-5) on the line is: y - (-xo-5) = 1(x - xo) ⇒ y = x - 2xo - 5
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