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The two lines have identical slopes if they are parallel to each other. If y1 = mx1 + c is the equation for one line then y2 = mx2 + d is the equation of a parallel line where c ≠ d. "m" is the slope which is the same value in both equations.
In most situations, the answer that is looked for is linear. However, since y=mx+b does not follow superposition, it is in fact, nonlinear. Proof: y1=mx1+b y2=mx2+b x3=Ax1+Bx2 y3=m(Ax1+Bx2)+b=mAx1+mAx2+b this does not equal Ay1+By2, making it nonlinear
First substitute the coordinates of (x1, y1) into the equation, then simplify the equation so it has y in terms of x. y - y1 = m(x - x1) y - y1 = mx - mx1 y = mx - mx1 + y1 y = mx + (y1 - mx1) y = mx + (C)
a unit vector is any vector with length or absolute value 1. A column vector is any vector written in a column of since we say an mxn matrix is m rows and n columns, a column vector is mx1 matrix.
What do you mean by "solve"? Do you want to rearrange it, solving for x? That would be: x = (y - b) / m Do you want to find it's derivative with respect to x? Then the answer is: y' = m Do you want to find it's indefinite integral? That'd be: ∫y dx = mx2/2 + bx + C