Step 1
<u>Find the equation of the line AB</u>
we know that
the equation of the line into point-slope form is equal to

Let

<u>Find the slope m</u>
we know that
the slope between two points is equal to

substitute



with the slope m and point A find the equation of the line AB

or
with the slope m and point B find the equation of the line AB

we will proceed to verify each case to determine the solution of the problem
Step 2
<u>Verify case A</u>
<u>Case A)</u> 
the slope of the line is 
but the point
-----> not lie on the line AB (see the graph)
therefore
the case A is not the solution
Step 3
<u>Verify case B</u>
<u>Case B)</u> 
the slope of the line is 
and the point
-----> is the point A
therefore
the case B is a solution
Step 4
<u>Verify case C</u>
<u>Case C)</u> 
the slope of the line is 
but the point
-----> not lie on the line AB (see the graph)
therefore
the case C is not the solution
Step 5
<u>Verify case D</u>
<u>Case D)</u> 
the slope of the line is
-----> the slope is not equal to the slope AB
and the point
-----> not lie on the line AB (see the graph)
therefore
the case D is not the solution
<u>the answer is</u>
The equation
is a point-slope form of the line AB