Question

Given two points on the line, input the equation of the line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.

(7, -3), (4, -8)

Answer 1

y = ax + b
-3 = 7a + b
b = -7a - 3
and
-8 = 4a + b
b = -4a - 8
then
-7a - 3 = -4a - 8
3a = 5
a = 5/3
b = - 4(5/3) - 8
b = - 20/3 - 24/3 = -44/3
y = (5/3)x - 44/3
3y = 5x - 44
5x - 3y = 44
..

Answer 2

For this one you want to do the same thing. You want to find the change in y and x. The change in y is -8-(-3)=-5 And the change in x is 4-7=-3 So your slope is 5/3. Using point slope again you have: y-(-3)=(5/3)(x-7)
y+3=5x3−353
Subtracting 3 gives you:
y=5x3−443
Putting the x on the left side and multiplying by 3 to get:
3y−5x=−44