Which equation is a point slope form equation for line AB ?y+2=−2(x−5)y+6=−2(x−1)y+1=−2(x−6)y+5=−2(x−2)

For this case we have that by definition, the equation of a line of the point-slope form is given by:[tex]y-y_ {0} = m (x-x_ {0})[/tex]Where:m: It's the slope[tex](x_ {0}, y_ {0}):[/tex]It is a point through which the line passesTo find the slope, we need two points through which the line passes, observing the image we have:[tex](x_ {1}, y_ {1}): (1,6)\\(x_ {2}, y_ {2}): (5, -2)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-2-6} {5-1} = \frac {-8} {4} = -2[/tex]Thus, the equation is of the form:[tex]y-y_ {0} = - 2 (x-x_ {0})[/tex]We choose a point:[tex](x_{0}, y_ {0}) :( 5, -2)[/tex]Finally, the equation is:[tex]y - (- 2) = - 2 (x-5)\\y + 2 = -2 (x-5)[/tex]Answer:[tex]y + 2 = -2 (x-5)[/tex]