how do I answer this question, what is the solution?

Question

Find the equation of the line in standard form that passes through the following points. Eliminate any fractions and simplify your answer. (-9, 11) and (4,-12)

Answer 1

Conventions needed for a standard form equation in 2 variables: Ax + By = C.

1. The coefficient of x must be ≥ 0. If not, multiply both sides of thevequation by -1.

2. The coefficients A and B must be integers. The constant C must also be an integer. If not multiply both sides by the common denominator.

3. The greatest common factor of A, B, and C is one. If not, divide both sides by the greatest common factor.

Answer 2

Slope = [-12 - 11] / [4 - (-9)] = -23/13

Equation of line has the form y = (-23/13)x + b.

Since (-9, 11) is a point on the line, we have 11 = (-23/13)(-9) + b

143 = 207 +13b So, 13b = --64

b = -64/13

Equation of line: y = (-23/13)x - 64/13

Multiply both sides by 13 to get 13y = -23x - 64

So, 23x + 13y = -64