Question

Graph the inequality on the axes below.
2, x, plus, 3, y, is greater than or equal to, 6
2x+3y≥6


were are the 2 points

Answer 1

To graph the inequality \(2x + 3y \geq 6\), we'll start by finding points that satisfy the corresponding equation \(2x + 3y = 6\).

### Step 1: Find the Boundary Line
1. **Intercepts**:
- **X-Intercept**: Set \(y = 0\):
\[
2x + 3(0) = 6 \implies 2x = 6 \implies x = 3
\]
So, the x-intercept is \((3, 0)\).

- **Y-Intercept**: Set \(x = 0\):
\[
2(0) + 3y = 6 \implies 3y = 6 \implies y = 2
\]
So, the y-intercept is \((0, 2)\).

### Step 2: Plot the Points
Plot the points \((3, 0)\) and \((0, 2)\) on the graph.

### Step 3: Draw the Boundary Line
Draw a solid line through the points \((3, 0)\) and \((0, 2)\) since the inequality is "greater than or equal to" (\(\geq\)), indicating that points on the line are included in the solution.

### Step 4: Determine the Shading Area
To find the area to shade (representing all solutions to the inequality):

1. **Test a Point**: A common test point is \((0, 0)\) (the origin):
\[
2(0) + 3(0) = 0 \quad \text{and} \quad 0 \geq 6 \quad \text{(false)}
\]
Since this point does not satisfy the inequality, we shade the area *above* the line (where the values of \(2x + 3y\) are greater than or equal to 6).

### Step 5: Final Graph
1. The line \(2x + 3y = 6\) is drawn as a solid line.
2. The region above this line is shaded to indicate that it includes all points \((x, y)\) satisfying \(2x + 3y \geq 6\).

### Summary
The critical points you determined were:
- Point A: \((3, 0)\) (x-intercept)
- Point B: \((0, 2)\) (y-intercept)

You can use these points to graph the inequality accurately on an appropriate set of axes.