We want to write the equation of the line passing through these two points in standard form.
First, we are going to do this in slope intercept form and then change the form to standard form, which is Ax + By = C
We will use the equation y = mx + b, and since we are given two points on the line we are going to determine the slope of the line by determining the change in the y coordinates
m = y sub2 - y sub1 divided by the change in the X coordinates x sub2 – x sub1
We will start by determining the slope
(1, -6) the 1 is x sub 1 and the 6 is y sub 1
(-7, 2) the -7 is x sub 2 and the 2 is y sub 2
2 - (-6) = 8
-7 -1 = -8
so equation now is m = -1
So now again referring back to the slope intercept of the line we now know y = -1 + b. We still have to determine b and the y intercept, and we can do this by using one of the given points and substituting in the value for y and x, and then solve for b. Since these points are on the line, they must satisfy this equation. If we use the first coordinates, we would substitute 1 for x and -6 for y.
-6 = -1 times x, which is 1 + b
b = -5
construct the line equation y = mx + b where m = -1 & b = -5
In slope intercept form the equation would be y = -x - 5
Now we want to write this in standard form now. We have to deal with two things. The x and y terms have to be on the left side and A and B and C have to be integers.
The standard form of a linear equation is Ax + By=CA x + By = C . Move all terms containing variables to the left side of the equation.
Add x to both sides of the equation.
y + x = -5
Reorder y & x
x + y = -5
. The first thing to do is to move the 
over to the other side because it has a common denominator with the other side. Doing that and at the same time combining them over their common denominator looks like this: 
. The best way to solve for x now is to cross-multiply to get 3(4-x)=-4(x-4). Distributing through the parenthesis is 12 - 3x = -4x + 16. Solving for x gives us x = 4. Of course when we sub a 4 back in for x we get real problems, don't we? Dividing by zero breaks every rule in math that there ever was! So, yes, the solution is extraneous.