Question

Graph the inequality on the axes below.
x, plus, 2, y, is greater than or equal to, minus, 4
x+2y≥−4

Answer 1

To graph the inequality \(x + 2y \geq -4\), we will follow these steps:

1. **Convert the inequality to an equation**: First, we treat the inequality as an equation to find the boundary line.
\[
x + 2y = -4
\]

2. **Find the x- and y-intercepts**:
- **x-intercept**: Set \(y = 0\):
\[
x + 2(0) = -4 \implies x = -4 \quad \text{(the point is } (-4, 0)\text{)}
\]
- **y-intercept**: Set \(x = 0\):
\[
0 + 2y = -4 \implies 2y = -4 \implies y = -2 \quad \text{(the point is } (0, -2)\text{)}
\]

3. **Graph the line**: Plot the points \((-4, 0)\) and \((0, -2)\) on the coordinate plane. Connect these points with a straight line. Since the inequality is "greater than or equal to" (≥), the line should be drawn as a solid line.

4. **Determine the shading**: To figure out which side of the line to shade, we can test a point not on the line. A common choice is the origin \((0, 0)\):

Substitute \(x = 0\) and \(y = 0\) into the inequality:
\[
0 + 2(0) \geq -4 \implies 0 \geq -4 \quad \text{(True)}
\]
Since the point \((0, 0)\) satisfies the inequality, we shade the region that includes \((0, 0)\), which is above the line.

5. **Final graph**:
- Draw the solid line representing \(x + 2y = -4\).
- Shade the area above the line, including the line itself.

This entire procedure will help you create the correct graph for the inequality \(x + 2y \geq -4\).