Question

What equation in slope intercept form represents the line that passes through the two points 2,5 (9,2

Answer 1

$General\ equation\ for\ line\ in\ slope\ intercept\ form:\\\\y=ax+b\\\\To\ find\ a\ and\ b\ substitude\ points\ (2,5),\ (9,2)\ into\ equation\\\\ \left \{ {{5=2a+b} \atop {2=9a+b}} \right. \\\\b=5-2a\ \ \ \ \ \ \ \ \ \ \ \ |from\ first\ equation\\\\2=9a+5-2a\ \ \ \ \ |substituting\ to\ the\ second\\2-5=7a\\7a=-3\\a=-\frac{3}{7}\\\\b=5-2\cdot(-\frac{3}{7})\\b=5+\frac{6}{7}=5\frac{6}{7}\\\\y=-\frac{3}{7}+5\frac{6}{7}$