The slope of a linear equation of the form Ax+By+C=0 (general form) is given by -\frac{A}{B

fecundavai3c

fecundavai3c

Answered question

2022-02-25

The slope of a linear equation of the form Ax+By+C=0 (general form) is given by AB. Could someone intuitively explain why we use this formula?
I've read that this is because the coefficient of x (coefficient of y) represent the "speed" at which x (y) increases and thus we can get the slope by dividing the "speed of x" by the "speed of y" - but I'm afraid it's not very intuitive to me.
Why do we use this formula and how is this equivalent to the more general slope formula,
slope=change in ychange in x

Answer & Explanation

Goodwin2ug

Goodwin2ug

Beginner2022-02-26Added 6 answers

The general equation of an affine line is y=mx+t with real values m,t.
Suppose you have two points on the line, say (x1,y1) and (x2,y2). Then when plugging in, the slope is
m=y2y1x2x1.

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