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 by using the slope formula..
slope(m) = (y2 - y1) / (x2 - x1)
(7,-3) x1 = 7 and y1 = -3
(4,-8) x2 = 4 and y2 = -8
now we sub
slope(m) = (-8 - (-3) / (4 - 7)
slope(m) = (-8 + 3) / -3
slope(m) = -5/-3 which equals 5/3
so our slope is 5/3
now you can either use point slope formula (y - y1 = m(x - x1) or you can use slope intercept form (y = mx + b). I prefer slope intercept form unless the problem specifically asks for point slope form, but that is just me.
y = mx + b
slope(m) = 5/3
you can use either of your sets of points
(7,-3) x = 7 and y = -3
now we sub
-3 = 5/3(7) + b
-3 = 35/3 + b
-3 - 35/3 = b
-9/3 - 35/3 = b
-44/3 = b
so your equation is : y = 5/3x - 44/3 but we need it in standard form
y = 5/3x - 44/3 --- multiply entire equation by 3
3y = 5x - 44 -- subtract 5x from both sides
-5x + 3y = -44 -- multiply by -1 to make x positive
5x - 3y = 44 ==> standard form

any questions ?