Question

Graph the inequality in the axes below. X+2y>-4

Answer 1

To graph the inequality x + 2y > -4, we first need to graph the corresponding equation x + 2y = -4.

To find the x-intercept, we set y = 0:

x + 2 * 0 = -4
x = -4

So, the x-intercept is at (-4, 0).

To find the y-intercept, we set x = 0:

0 + 2y = -4
2y = -4
y = -2

So, the y-intercept is at (0, -2).

Now, we can plot the x-intercept (-4, 0) and y-intercept (0, -2) on the graph:

{{NumberLine|({-4} , 0) ; (0 , -4)}}

Next, we need to determine whether to shade the region above or below the line. We can pick any point not on the line to determine which region is the solution. Let's use the point (1, 1):

1 + 2 * 1 = 3
3 > -4

Since the inequality is true for (1, 1), we shade the region above the line.

The completed graph looks like this:
{{graph(200, 200, -10, 10, -10, 10, y < -0.5x -2)}}