For this case we have the following equation:

That can be rewritten in the form 
Where:
- m is the slope of the line
So, we have:

Where:
 is the slope
 is the slope
 is the cut point
 is the cut point
Carlota has the following points:
(-1, 3) and (2, 9)
To know if the line  passes through these points, we must replace them in the equation and the equality must be fulfilled. So:
 passes through these points, we must replace them in the equation and the equality must be fulfilled. So:
Point (-1, 3):
Substituting:

 It's false, equality is not met. The point (-1, 3) does not go through the line.
 It's false, equality is not met. The point (-1, 3) does not go through the line.
The equation written by Carlota is erroneous, the procedure to follow is:
Given and
 and , we find the slope:
, we find the slope:




We observe that the slope found by Carlota is the same. Let's see cut point "b". For this we substitute any of the points given in the equation:

Substituting (2,9) we have:

Thus, Carlota's error was at the cut-off point. The correct equation of the line that passes through the given points is 
Answer:
The correct equation of the line that passes through the given points is 
Carlota's mistake was at the cutoff point