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

(7,-3)(4,-8)
slope(m) = (y2 - y1) / (x2 - x1)
slope(m) = (-8 - (-3) / (4 - 7) = (-8 + 3) / -3 = -5/-3 = 5/3

y = mx + b
slope(m) = 5/3
(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 ur equation in slope int form is : y = 5/3x - 44/3
but we need it in standard form...

y = 5/3x - 44/3
-5/3x + y = - 44/3...multiply by -1
5/3x - y = 44/3...multiply by 3
5x - 3y = 44 <== standard form

Answer 2

The slope: $m=\dfrac{y_2-y_1}{x_2-x_1}$

$(7;-3)\to x_1=7\ and\ y_1=-3\\(4;-8)\to x_2=4\ and\ y_2=-8$

subtitute

$m=\dfrac{-8-(-3)}{4-7}=\dfrac{-8+3}{-3}=\dfrac{-5}{-3}=\dfrac{5}{3}$

The slope-point form: $y-y_1=m(x-x_1)$

subtitute

$y-(-3)=\dfrac{5}{3}(x-7)\\\\y+3=\dfrac{5}{3}x-\dfrac{35}{3}\ \ \ |multiply\ both\ sides\ by\ 3\\\\3y+9=5x-35\ \ \ |subtract\ 3y\ from\ both\ sides\\\\5x-3y-35=9\ \ \ \ |add\ 35\ to\ both\ sides\\\\\boxed{5x-3y=44}$