Question

Find the equation of the line passing through the given points. Express the equation in standard form.

Answer 1

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