How can we derive the standard form of the linear equation: Ax+By+C=0? What do "A", "B" and "C" in the standard form of the linear equation mean? As in the point-slope form of the linear equation: y−y0=m(x−x0), m is the slope, and x, y are the coordinates of any point. Likewise,x0,y0, are the coordinates of the given point.

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How can we derive the standard form of the linear equation:  Ax+By+C=0? What do &quot;A&quot;, &quot;B&quot; and &quot;C&quot; in the standard form of the linear equation mean? As in the point-slope form of the linear equation:  y−y0=m(x−x0), m is the slope, and x, y are the coordinates of any point. Likewise,x0,y0, are the coordinates of the given point.

Nicolle Newman · Accepted Answer

Let&#039;s say we start with the point-slope form y−y0=m(x−x0), where (x,y) represents any point on the line, and (x0,y0) represents a given point on the line, and m is the given slope of the line. Now, y−y0=m(x−x0)⇔y−y0=mx−mx0 ⇔y−y0−mx−mx0=0 ⇔(−m)x+y+(−y0−mx0)=0 Now, we can simply let A=−m,B=1,C=(−mx0−y0), which means that y+(−m)x+(−y0−mx0)=0⟺Ax+By+C=0

How can we derive the standard form of the linear equation: Ax+By+C=0? What do "A", "B" an

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