Question

x+2y<4 graph the inequality

Answer 1

To graph the inequality x + 2y < 4, we can start by graphing the equation x + 2y = 4.

First, let's find the x and y-intercepts of the graph.

Setting x = 0, we have:
0 + 2y = 4
2y = 4
y = 2
So, the y-intercept is (0, 2).

Setting y = 0, we have:
x + 2(0) = 4
x + 0 = 4
x = 4
So, the x-intercept is (4, 0).

Plotting the x and y-intercepts on the coordinate plane, we get:

(Note: Each line represents one unit on the graph.)

Now, we just need to determine which side of the line to shade based on the inequality x + 2y < 4.

To do this, we can choose a point not on the line and substitute its x and y-values into the inequality to see if it is a true statement.

Let's choose the point (0, 0) since it is conveniently on the graph. Substituting these values into the inequality, we get:
0 + 2(0) < 4
0 < 4
This is true, so we shade the side of the line that (0, 0) lies on.

In this case, since the inequality is less than (<), we shade below the line.

The shaded region represents all the points that satisfy the inequality x + 2y < 4.

The graph should look like this:

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I apologize if the graph does not appear accurately as I have tried my best to describe it in text form.