Algebra Question About Equation of Line?

Question

The question is:

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

The linear equation is in standard form is Ax + By = C, where A, B, and C are real numbers and A and B both are not zero. All linear equations can be written in standard form.

First find the line equation using point-slope form y - y1 = m (x - x1), where m is slope.

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

The line equation is y - y1 = 5/3 (x - x1)

y- (-3)) = 5/3 ( x - 7)

y + 3 =  5/3 (x - 7)

Eliminate fractions by multiplying ech side by 3

3y + 9 = 5x - 35

Subtract 3y from each side

5x - 3y = -44

The standard form equation is 5x - 3y = -44