Question

how to graph the inequality x+2y ≤-4
give coordinate

Answer 1

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

### Step 1: Convert the Inequality to an Equation
Start by converting the inequality to an equation for easier graphing. The corresponding equation is:
\[
x + 2y = -4
\]

### Step 2: Find the Intercepts
To graph the line, find the x-intercept and y-intercept.

1. **X-intercept**: Set \(y = 0\) in the equation:
\[
x + 2(0) = -4 \implies x = -4
\]
So, the x-intercept is \((-4, 0)\).

2. **Y-intercept**: Set \(x = 0\) in the equation:
\[
0 + 2y = -4 \implies 2y = -4 \implies y = -2
\]
So, the y-intercept is \((0, -2)\).

### Step 3: Plot the Line
Plot the points \((-4, 0)\) and \((0, -2)\) on the coordinate plane. Next, draw a line through these points. Because the original inequality is \(\leq\), you will use a solid line to indicate that points on the line are included in the solution.

### Step 4: Shade the Region
Since the inequality is \(x + 2y \leq -4\), you want to shade the region below the line. This is the region where the y-values satisfy the inequality.

### Summary Coordinate Points
You can use the following coordinates that represent points that satisfy the inequality:

1. A point below the line (for example, \((-5, 0)\)):
\[
-5 + 2(0) = -5 \leq -4 \quad \text{(True)}
\]
2. Another point below the line (for example, \((-4, -3)\)):
\[
-4 + 2(-3) = -4 - 6 = -10 \leq -4 \quad \text{(True)}
\]

### Final Note
You can pick many coordinates below the line that will satisfy the inequality. Just ensure that they satisfy \(x + 2y \leq -4\).