How do you graph the inequality 2x y 4?

To graph the inequality 2x < y + 4, we first need to rearrange it in a more standard form. Let's express it as:

2x – y < 4

Next, we’ll replace the inequality with an equality to find the boundary line:

2x – y = 4

To graph this line, we’ll find the x and y-intercepts:

• For the x-intercept, set y = 0:
• 2x – 0 = 4 -> 2x = 4 -> x = 2. So, the x-intercept is (2, 0).
• For the y-intercept, set x = 0:
• 2(0) – y = 4 -> -y = 4 -> y = -4. So, the y-intercept is (0, -4).

Now we can graph these two points (2, 0) and (0, -4) on a coordinate plane. Once we connect them with a straight line, we must determine the type of line to draw:

Since our original inequality is ‘less than’ (not ‘less than or equal to’), we draw a dashed line. This indicates that points on the line are not included in the solution set.

Finally, we need to shade the appropriate region of the graph. Because our inequality is 2x – y < 4, we shade below the line, which represents all the points where the inequality holds true.

In summary, the steps to graph the inequality 2x – y < 4 are:

1. Rearrange the inequality if necessary.
2. Find the intercepts to graph the boundary line.
3. Draw a dashed line since the inequality is not inclusive.
4. Shade the region that satisfies the inequality.