how do you convert two points to standard form(ax+by=c)?

1st: compute the slope(m) of the line passing through those points.

2nd: substitute the slope into the point-slope form of the equation of a line: (x-x1)=m(y-y1).

3rd: rearrange into the standard form

First get y on the LHS:

by = -ax + c

y(x) = (-a/b)x + c/b = mx + d

y(6) = m(6) + d = -1

y(-3) = m(-3) + d = 7

Subtract the second from the first:

9m = -8

m = -8/9 = -a/b by the eqn for y(x) above

(-8/9)(-3) + d = 7

8/3 + d = 7

d = 7 - 8/3 = 21/3 - 8/3 = 13/3 = c/b from above

a = 8, b = 9, c = 13/3 (3/3)b = 39/9 b, so c = 39

8x + 9y = 39 is the answer

y-(-1)/x-6 = 7-(-1)/-3-6

y+1/x-6 = 7+1/-9

-9(y+1) = 8(x-6)

-9y-9 = 8x-48

8x+9y = 48-9

8x+9y = 39

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