I am stucked on the following challenge: "If the line determined by two distinct points (x1,y1) and (x2,y2) is not vertical, and therefore has slope (y2−y1)(x2−x1), show that the point-slope form of its equation is the same regardless of which point is used as the given point." Okay, we can separate (x0,y0) from the form to get:y(x2−x1)−x(y2−y1)=y0(x2−x1)−x0(y2−y1)But how exclude this point (x0,y0) and leave only x,y,x1,y1,x2,y2 in the equation? UPDATE: There is a solution for this challenge:(y1−y2)x+(x2−x1)y=x2y1−x1y2From the answer I found thaty2(x−x1)−y1(x−x2)=y(x2−x1)but why this is true?

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I am stucked on the following challenge: &quot;If the line determined by two distinct points (x1,y1) and (x2,y2) is not vertical, and therefore has slope (y2−y1)(x2−x1), show that the point-slope form of its equation is the same regardless of which point is used as the given point.&quot; Okay, we can separate (x0,y0) from the form to get:y(x2−x1)−x(y2−y1)=y0(x2−x1)−x0(y2−y1)But how exclude this point (x0,y0) and leave only x,y,x1,y1,x2,y2 in the equation? UPDATE: There is a solution for this challenge:(y1−y2)x+(x2−x1)y=x2y1−x1y2From the answer I found thaty2(x−x1)−y1(x−x2)=y(x2−x1)but why this is true?

Warenberg56i · Accepted Answer

Thanks to saulspatz, the solution is to simply show, that whether we are using (x1,y1)or(x2,y2) as the given point, the equation does not change. So both equations: y−y1=m(x−x1) y−y2=m(x−x2) reduce to the (y1−y2)x+(x2−x1)y=x2y1−x1y2

I am stucked on the following challenge: "If the line determined by two distinct points (x_1,y_1)

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