Question

How do you graph the inequality `2x + y > 1`?

Answer 1

`y > -2x+1` is easier to plot.
Draw a dotted line and shade above the line.

Explanation:

The first step is to change the inequality into an easier form.

`y > -2x+1`

From this we have the following:

• The `y`-intercept is at the point `(0, 1)`

• The slope is `-2`

• The inequality sign is `>` so the graph will be a dotted line.

• The area above the line will be shaded

To draw the graph:

• Find the `x`-intercept by putting `y=0`
  `0= -2x+1`
  `2x=1`
  `x =1/2`

• Plot the point `(1/2,0)`

• Plot the y-intercept at the point `(0,1)`

From the y-intercept `"rise"/"run"` will give us 2 units up and 1 to the left.

Repeat this process at least 3 times to get a line of points.

Draw a dotted line and shade the area above the line.

graph{y > -2x+1 [-1.302, 3.698, -0.73, 1.77]}