Question

What is the system of inequalities associated with the following graph?
3x + y ≥ -3
x + 2y ≤ 4

-3x – y ≥ -3
x + 2y ≤ 4

3x + y ≥ -3
x – 2y ≥ 4

3x – y ≤ 3
x – 2y ≥ 4

Answer 1

One line passes through the points (-2,3) and (0,-3) , it means the y intercept is b=-3

and slope m = $\frac{(-3-3)}{0-(-2)}$

$= \frac{-6}{2}= -3$

So the equation of line will be $y= -3x -3$

And the inequality should be $y\geq -3x-3$

Or $3x +y \geq -3$

And the other line passes through (-2,3) and (0,2)

So the y intercept is b=2

and the slope is $m= \frac{2-3}{0-(-2)} = \frac{-1}{2}$

So the equation of line will be $y= \frac{-1}{2} x +2 and the inequality should be y \leq \frac{-1}{2} x+2$

Or

$2y +x \leq 4$

So answer is $3x +y \geq -3, x+2y\leq 4$

Answer 2

Answer: d

Step-by-step explanation: