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Answer:
5x +9y = -49
Step-by-step explanation:
For two points (x1, y1) and (x2, y2), we can define Δy = y2 -y1 and Δx =x2 -x1. Then the standard form equation of a line through those points can be written ...
(Δy)x -(Δx)y = (Δy)x1 -(Δx)y1
Here, we have Δy = -1-(-6) = 5, and Δx = -8-1 = -9, so our equation can be ...
5x +9y = 5(1) +9(-6) = -49
5x +9y = -49
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Additional comment
Standard form requires the leading coefficient be positive, and all coefficients be mutually prime. If the points are chosen so that y2 > y1, then the first condition is easily met. To meet the second condition, sometimes a common factor must be divided from all of the coefficients to reduce them to standard form.
This form can be derived from the fact that the slope of a line is the same everywhere:
Δy/Δx = (y -y1)/(x -x1) ⇒ (Δy)(x -x1) = (Δx)(y -y1) ⇒ above equation
