Question

What is the equation of the line?

Answer 1

3rd choice

Explanation:

y = mx + b

Look at where the line crosses the y-axis. That is the y-intercept. It is 2, so b = 2, and you have

y = mx + 2

Now we need the slope, m.

Start at (0, 2). Go up 1 and right 2.

slope = m = rise/run = 1/2

Now you have

y = 1/2 x + 2

Answer: 3rd choice

Answer 2

`c)y=(1)/(2)x+2`

Explanation:

`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)=(rise)/(run)=(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=(1-3)/(-2-2)=(-2)/(-4)=(1)/(2)\\Hence,\\m=(1)/(2)\\`

`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=((1)/(2))x+(+2)\\y=(1)/(2)x+2`