How do you graph the inequality #y<=-2/3x+4#?

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality. The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-4)^2-0.05)((x-3)^2+(y-2)^2-0.05)(y + (2/3)x-4)=0 [-10, 10, -5, 5]}

Now, we can shade the left side of the line.

graph{(y + (2/3)x-4) <= 0 [-10, 10, -5, 5]}

To graph the inequality ( y \leq -\frac{2}{3}x + 4 ), first, graph the line ( y = -\frac{2}{3}x + 4 ) as if it were an equation. Then, since the inequality includes "less than or equal to," you shade the region below the line, including the line itself, because the points on the line satisfy the inequality.