For this case we have that the point slope equation of a line is given by:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
Where "m" is the slope and [tex](x_ {0}, y_ {0})[/tex] is a point belonging to the line.
Then, we find the slope, for this we need two points:
[tex](x_ {1}, y_ {1}) = (10,5)\\(x_ {2}, y_ {2}) = (4, -7)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}\\m = \frac {-7-5} {4-10}\\m = \frac {-12} {- 6}\\m = 2[/tex]
We build the equation by choosing any of the points:
[tex]y-5 = 2 (x-10)[/tex]
Answer:
[tex]y-5 = 2 (x-10)[/tex]
Option B
