How do you graph the inequality x + 2y < 4?

Graphing the Inequality x + 2y < 4

Graphing the inequality x + 2y < 4 involves several steps:

1. Rewrite the Inequality: Start by isolating y. You can do this by rearranging the terms:

2y < 4 - x

Now, divide by 2 to solve for y:

y < 2 - 0.5x

2. Graph the Boundary Line: The boundary line is found by treating the inequality as an equation: x + 2y = 4. To graph this line:
• Find the x-intercept (set y = 0):

0 + 2y = 4  →  y = 2  ⟹  (0, 2)

• Find the y-intercept (set x = 0):

x + 2(0) = 4  →  x = 4  ⟹  (4, 0)

Plot these points (0, 2) and (4, 0) on a graph, and draw a dashed line between them to indicate that this line is not included in the solution.

3. Shade the Appropriate Region: Since the original inequality is <, you will shade the area below the line. This area represents all points (x, y) that satisfy the inequality.

By following these steps, you’ll successfully graph the inequality x + 2y < 4 and visually represent the solution set.