To graph the inequality x + 2y < 4, you first need to convert the inequality into an equation. The equation that corresponds to the inequality is:
x + 2y = 4
Next, you can find points on the line represented by this equation. To do this, you can set x to 0 (to find the y-intercept) and solve for y:
0 + 2y = 4 → 2y = 4 → y = 2
This gives you the point (0, 2). Now, set y to 0 (to find the x-intercept) and solve for x:
x + 0 = 4 → x = 4
This gives you another point (4, 0). Now you have the points (0, 2) and (4, 0) that you can plot on a graph.
Next, draw a straight line through these two points. Since the original inequality is strict (x + 2y < 4, not ≤), you will use a dashed line to indicate that points on the line are not included in the solution set.
Finally, you need to determine which side of the line is part of the solution to the inequality. You can do this by selecting a test point that is not on the line — a common choice is (0, 0). Plug this point into the inequality:
0 + 2(0) < 4 → 0 < 4
Since this statement is true, you shade the region of the graph that contains the point (0, 0). This shaded area represents all the points (x, y) that satisfy the inequality x + 2y < 4.