Answer:
[tex]c)y=\frac{1}{2}x+2[/tex]
Step-by-step explanation:
[tex]We\ know\ that,\\The\ equation\ of\ a\ graph\ is\ given\ by\ the\ formula:\\y=mx+b,\ where\ m\ is\ the\ slope\ of\ the\ graph,\ and\ b\ is\ the\ y-intercept;\\Here,\\First,\\Lets\ calculate\ the\ slope\ of\ the\ graph:\\We\ also\ know\ that,\\Slope(m)=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}\\Lets\ consider\ any\ two\ points\ which\ lie\ on\ the\ line:\\(2,3),(-2,1)\\Hence,\\The\ slope\ of\ the\ given\ line=\frac{1-3}{-2-2}=\frac{-2}{-4}=\frac{1}{2}\\Hence,\\m=\frac{1}{2}\\[/tex]
[tex]Now,\\The\ y-intercept\ is\ the\ point\ at\ which\ the\ graph\ intersects\ the\ whole\ y-axis.\\Hence,\\Here,\\The\ line\ of\ the\ graph\ cuts\ the\ y-axis\ at\ (0,2).\\The\ y-intercept\ of\ the\ line=2\\Hence,\\The\ equation\ of\ the\ line:\\y=(\frac{1}{2})x+(+2)\\y=\frac{1}{2}x+2[/tex]
