Which equation is a point slope form equation for line AB ? A。 y+1=−23(x−4) B。y+1=−32(x−4) C。y+1=23(x−4) D。 y+1=32(x−4)

Accepted Solution

Answer: The correct option is A.Explanation:From the given figure it is noticed that the coordinates of point A are (4,-1) and the coordinates of B are (-2,3).The slope form of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]The line AB passing through two points A(4,-1) and B(-2,3).Using the above formula,[tex]y-(-1)=\frac{3-(-1)}{-2-4}(x-4)[/tex][tex]y+1=\frac{3+1}{-6}(x-4)[/tex][tex]y+1=\frac{4}{-6}(x-4)[/tex][tex]y+1=-\frac{2}{3}(x-4)[/tex]Therefore, the option A is correct.