Question

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

Explanation:

Step1: Rewrite in slope - intercept form

First, rewrite $2x + 3y\leq6$ as $y\leq-\frac{2}{3}x + 2$.

Step2: Graph the boundary line

The boundary line is $y =-\frac{2}{3}x+2$. The y - intercept is 2 and the slope is $-\frac{2}{3}$. Plot the y - intercept (0, 2) and use the slope to find another point. From (0, 2), move down 2 units and right 3 units to get the point (3, 0). Draw a solid line since the inequality is $\leq$.

Step3: Test a point

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

Answer:

Graph a solid line $y =-\frac{2}{3}x + 2$ and shade the region below the line including the line itself.