Which equation is a point slope form equation for line AB ?

Answer:Option Cequation :  [tex]y-5=\frac{3}{4} (x-6)[/tex]Step-by-step explanation:Point slope form Equation states that the equation of a straight line in the form [tex]y-y_{1}=m(x-x_{1})[/tex];   where m is the slope of the line. We have to find the equation for line AB.From the figure, we have The coordinate of [tex]A(x_{2} , y_{2})[/tex] =  ( -2, -1) and  [tex]B(x_{1} , y_{1})[/tex] = (6 ,5)First find the value of m:[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]Now, substitute the points of A and B into slope m:   [tex]m = \frac{-1-(5)}{-2-(6)}[/tex] or[tex]m =\frac{-6}{-8} = \frac{3}{4}[/tex]Then, the equation of line: [tex]y-y_{1}=m(x-x_{1})[/tex]Substitute the value of slope in above equation and the coordinates of [tex](x_{1} , y_{1})[/tex] we have, [tex]y-5=\frac{3}{4} (x-6)[/tex]Therefore, the equation for the point slope form is, [tex]y-5=\frac{3}{4} (x-6)[/tex]