Slope of the line AB is $$ - \frac{2}{3}.$$  Co-ordinates of points A and B are (x, -3) and (5, 2) respectively. What is the value of x?

Given,

$$\eqalign{ & m = \frac{{ - 2}}{3} \cr & m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} \cr & \Rightarrow \frac{{ - 2}}{3} = \frac{{2 + 3}}{{5 - x}} \cr & \Rightarrow \frac{{ - 2}}{3} = \frac{5}{{5 - x}} \cr & \Rightarrow - 10 + 2x = 15 \cr & \Rightarrow 2x = 25 \cr & \Rightarrow x = 12.5 \cr} $$