Question

A line passes through (6,3), (8,4), and (n, -2). Find the value of n

Answer 1

`General\ equation\ for\ line\ in\ slope\ intercept\ form:\\y=ax+b\\\\To\ find\ a\ and\ b\ substitude\ points\ (6,3),\ (8,4)\ into\ equation\\\\ \left \{ {{3=6a+b}\ \ \ \ \atop 4=8a+b\ } \right.\\\\ \left \{ {{3=6a+b}\ \ \ \ \atop {-4=-8a-b\}} \right.\\+----\\-1=-2a\ \ |:-2\\\\a=(1)/(2)\\\\3=6\cdot(1)/(2)+b\\3=3+b\\b=3-3=0\\y=(1)/(2)x\\\\To\ find\ value\ of\ n\ we\ have\ to\ substitute\ (n,-2)\ to\ equation:\\\\-2=(1)/(2)n\ \ \ \ \ \ \ \ \ |\cdot2\\\\n=-4`