Question

What is a line passing through the points (1, -1) and (9, 3) in equation form?

Answer 1

`x-2y=3`

Explanation:

`We\ are\ given,\\Line\ passes\ through\ the\ points\ (1,-1) and (9,3). Hence,\ this\ means\ that\ the\\ points\ are\ indeed\ solutions\ of\ the\ equation,\ which\ represents\ the\ line.\\Hence,\\We\ know\ that,\\The\ equation\ of\ a\ line\ (Point-Slope)\ is\ given\ by:\\y-y_1=m(x-x_1),\ where\ m\ is\ the\ slope\ of\ the\ graph.`

`So\ first,\\Lets\ find\ the\ Slope\ of\ the\ Graph.\\Slope(m)=(Rise)/(Run)=(y_2-y_1)/(x_2-x_1)\\Hence,\\Here,\\Considering\ (1,-1)\ as\ the\ First\ Point\ and\ (9,3)\ as\ the\ Second\ Point,\ we\ have:x_1=1,x_2=9\ and\ y_1= -1, y_2=3\\Plugging\ the\ values\ in\ the\ Equation\ for\ the\ Slope,\ we\ have:\\`

`m=(y_2-y_1)/(x_2-x_1)=(3-(-1))/(9-1)=(3+1)/(9-1)= (4)/(8)=(1)/(2)\\Hence,\\Coming\ back\ to\ our\ Point-Slope\ Formula\ for\ the\ equation:\\\ We\ already\ have:\\y-y_1=m(x-x_1)\\Substituting\ m=(1)/(2) , x_1=1,\ y_1=-1,\ we\ have: \\y+1=(1)/(2)(x-1)\\\therefore 2(y+1)=x-1\\\therefore 2y+2=x-1\\\therefore 2y-x=-3\\Multiplying\ with\ (-1)\ on\ both\ sides:\\\therefore x-2y=3\\Hence,\\x-2y=3,\ is\ our\ desired\ equation.`