Question

How do you graph the equation `y=1/2x+2`?

Answer 1

See below:

Explanation:

There are a couple of ways to graph this - you can do a table of points or you can use the slope-intercept form of the equation and generate 2 points. Either way, once you have a couple of points, a straight-edge will help connect them and complete the graph.

Looking at the table method first, let's use `x=0, x=2` because using 0 is usually pretty straightforward and using 2 will help deal with the fraction `1/2`:

`x=0, y=2; x=2, y=3` - we can plot those and connect them and let them fly off into infinity in both directions!

The other way to do this is to use the slope-intercept form of the line (and since the equation is given in slope-intercept already, we're good to go). Slope-intercept form tells us the slope (`m`) and the y-intercept (`b`) in this way:

`y=mx+b`

So first we can see that the y-intercept in our equation, `b=2`. The value of `x` when the graph intersects the y-axis is 0, so we have a point `x=0, y=2`.

The slope tells us how the graph moves. The numerator tells us how many the graph goes up and the denominator tells us how many it moves to the right. So we'll move up 1 and to the right 2, which gives us point `x=2, y=3`. Again, we now have 2 points so we can use a straight-edge to connect them and let them run off into infinity in both directions.

The graph itself will look like this:

graph{(x/2)+2 [-10, 10, -5, 5]}