Question

question graph the inequality on the axes below. 2x + 3y ≤ 3

Explanation:

Step1: Find the x - intercept

Set \(y = 0\) in the equation \(2x+3y = 3\). Then \(2x=3\), so \(x=\frac{3}{2}=1.5\). The x - intercept is the point \((1.5,0)\).

Step2: Find the y - intercept

Set \(x = 0\) in the equation \(2x + 3y=3\). Then \(3y=3\), so \(y = 1\). The y - intercept is the point \((0,1)\).

Step3: Draw the line

Draw a solid line (since the inequality is \(\leq\)) passing through the points \((1.5,0)\) and \((0,1)\).

Step4: Test a point

Test the point \((0,0)\) in the inequality \(2x+3y\leq3\). Substitute \(x = 0\) and \(y = 0\): \(2(0)+3(0)=0\leq3\). Since this is true, shade the region that contains the point \((0,0)\).

Answer:

Draw a solid line passing through \((1.5,0)\) and \((0,1)\) and shade the region below (including the line) the line that contains the origin \((0,0)\).