#### Determine the ratio in which the line 2x + y - 4 = 0 divides the line segment joining A(2,-2) and B(3,7)

$Let\;the\;ratio\;be\;k:1\;and\;P\;be\;the\;point\;where\;lines\;intersect\\* Using\;section\;formula,\;we\;get\;P=(\frac{3k+2}{k+1},\frac{7k-2}{k+1})\\*Since\; 2x+y-4=0\; divides\;the\;line\;at\;P,\;So\;the\;point\;P\;lie\;on\\*this\;line,\; therefore\;we\;have\\*\Rightarrow 2(\frac{3k+2}{k+1})+(\frac{7k-2}{k+1})-4=0\\*\Rightarrow 6k+4+7k-2-4k-4=0\\*\Rightarrow 9k=2\\* \Rightarrow k=\frac{2}{9}\\*Hence, \;the \;ratio \;is \;2:9$