Question

What is the answer for this? please help!

Answer 1

For this case, the first thing to do is find the equation of the line, of the form$y = mx + b$

Where:

m: It's the slope

b: It is the cutoff point with the y axis

$m=\frac{y2-y1}{x2-x1}\\m=\frac{-2-1}{0-1}\\m=\frac{-3}{-1}\\m=3$

Thus, the equation is:

$y = 3x + b$

Replace any of the points to find b:

$1 = 3 (1) + b\\1 = 3 + b\\b = 1-3\\b = -2$

Finally, the equation is:

$y = 3x-2$

Now, we must determine the sign of inequality.

We have two possible options, in each one we will substitute a point in the region to know if it is fulfilled:

• $y\geq3x-2\\Point\ (0,0)\\0\geq3 (0) -2\\0\geq- 2$

Is fulfilled.

• $y \leq3x-2\\Point\ (0,0)\\0 \leq0-2\\0\leq- 2$

It is not fulfilled Therefore, the shaded region corresponds to:

$y\geq3x-2$

Answer:

$y\geq3x-2$