problem on coordinates

Given a point P(8,1) on Segment AB with A(-2,3), find the coordinates of B if AP/AB= 2/3

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$m={\color{black}\frac{y_P-y_A}{x_P-x_A}=-\frac{2}{10}=-}0.2$

$f(x)=m(x-x_P)+y_P$

$f(x)=-0.2(x-8)+1$

$f(x)=-0.2x+2.6$

$\color{blue}(x_P-x_A):(x_B-x_A)=2:3\\ 2x_B-2x_A=3x_P-3x_A\\ 2x_B=3x_P-3x_A+2x_A\\ 2x_B=3\cdot 8-3\cdot (-2)+2\cdot (-2)\\ x_B=12+3-2$

$x_B=13$

$y_B=-0.2\cdot 13+2.6$

$y_B=0$

The coordinates of B: $B\ (13,0)$

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