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

First you need to find the slope....to do this we will use the slope formula :
slope(m) = (y2 - y1) / (x2 - x1)
(7,-3) x1 = 7 and y1 = -3
(4,-8) x2 = 4 an y2 = -8

now lets sub our info into the formula to find the slope...
slope(m) = (-8 - (-3) / (4 - 7)
m = (-8 + 3) / -3
m = -5/-3
m = 5/3

so our slope is 5/3.

Now we will use point slope formula :
y - y1 = m(x - x1)
slope(m) = 5/3
you can use either of your sets of points....I will use (7,-3)
(7,-3) x1 = 7 and y1 = -3
now lets sub...
y - (-3) = 5/3(x - 7) -- distribute through the parenthesis
y + 3 = 5/3x - 35/3 -- subtract 3 from both sides
y = 5/3x - 35/3 - 3 -- common denominator is 3
y = 5/3x - 35/3 - 9/3
y = 5/3x - 44/3 <-- slope intercept form

now we need it in standard form : Ax + By = C
y = 5/3x - 44/3 -- subtract 5/3x from both sides
-5/3x + y = -44/3 -- multiply the equation by 3 to get rid of fractions
-5x + 3y = -44 -- now multiply the equation by -1 to make x positive
5x - 3y = 44 <-- standard form