Assume you want to know what is the formula of the gradient of the function in multivariable calculus.
Let F be a scalar field function in n-dimension. Then, the gradient of a function is:
∇F = <fx1 , fx2, ... , fxn>
In the 3-dimensional Cartesian space:
∇F = <fx, fy, fz>
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basically the reciprocal of the original lines gradient is going to be the gradient for the perpendicular line (remember the signs should switch). For example if i had a line with the gradient of 3, then the gradient of the perpendicular line will be -1over3. But if the line had the gradient of -3, then the line perpendicular to that line will have the gradient 1over3.
y2 - y1-------- = Gradient
If A = (xa, ya) and B = (xb, yb) and xa is not equal to xb, then gradient of AB = (ya - yb)/(xb - xb).If xa = xb then the gradient is undefined.
A gradient requires two variables. There is information on only one.
Gradients can be worked out by: 1. gradient formula, suppose the two points are (x1,y1); (x2,y2) then the gradient=(y2-y1)/(x2-x1) 2. rise/run Intercepts can be found by: 1. to find the x-intercept substitute y=0 into the equation of the line 2. to find the y-intercept substitute x=0 into the equation of the line