Question

graph the following inequality. 2x + 3y ≤ 6 use the graphing tool to graph the inequality. click to enlarge graph

Explanation:

Step1: Find x - intercept

Set \(y = 0\), then \(2x+3\times0\leq6\), so \(2x\leq6\) and \(x = 3\). The x - intercept is \((3,0)\).

Step2: Find y - intercept

Set \(x = 0\), then \(2\times0 + 3y\leq6\), so \(3y\leq6\) and \(y = 2\). The y - intercept is \((0,2)\).

Step3: Draw the line

The equation of the boundary line is \(2x + 3y=6\), which is a straight - line passing through \((3,0)\) and \((0,2)\). Since the inequality is \(\leq\), the boundary line is solid.

Step4: Test a point

Test the point \((0,0)\). Substitute \(x = 0\) and \(y = 0\) into the inequality \(2x+3y\leq6\), we get \(2\times0+3\times0=0\leq6\), which is true. So, shade the region that contains the origin.

Answer:

Graph a solid line passing through \((3,0)\) and \((0,2)\) and shade the region that contains the origin.