Question

Which system of inequalities is represented on this graph?

Answer 1

Answer:

It is the second answer choice

Step-by-step explanation:

Answer 2

Answer:

The correct option is 2.

Step-by-step explanation:

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$, then the equation of line is

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

From the given graph it is clear that the solid line passes through the points (0,2) and (1,0). So, the related equation of solid line is

$y-2=\frac{0-2}{1-0}(x-0)$

$y-2=-2x$

Add 2 on both sides.

$y=-2x+2$

The sign of inequality must be ≤ because the points on the line are included in the solution set and the shaded region is below the line.

$y\leq -2x+2$                 .... (1)

From the given graph it is clear that the solid line passes through the points (0,-1) and (1,0). So, the related equation of solid line is

$y-(-1)=\frac{0-(-1)}{1-0}(x-0)$

$y+1=x$

Subtract 1 from both sides.

$y=x-1$

The sign of inequality must be < because the points on the line are not included in the solution set and the shaded region is below the line.

$y$                 .... (2)

The system of inequalities is

$y\leq -2x+2$

$y$

Therefore, the correct option is 2.