Question

There are four inequalities that define the region R.

Answer 1

Answer:

$y\geq 0\\y\geq \frac{3}{2}x-3\\ y\leq -x+3$

Step-by-step explanation:

The region R is surrounded by 4 lines, the first one is y=x+1, the second one is y=0 or the axis x, and the third and fourth one need to be calcualted.

To find the equation of a line through the points (x1,y1) and (x2, y2) we can use the following equation:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Then, our third line is going to be the line that passes through the points (2,0) and (4,3), so the equation is:

$y=\frac{3-0}{4-2}(x-2)\\y=\frac{3}{2}x-3$

Our fourth line is the line that passes through the points (3,0) and (0,3), so the equation is:

$y=\frac{3-0}{0-3}(x-3)\\y=-x+3$

Then we can say that the other three inequalities are:

$y\geq 0\\y\geq \frac{3}{2}x-3\\ y\leq -x+3$