Question

Which system of linear inequalities is represented by the graph?

Answer 1

Answer:

The graph represent the system of linear inequalities $y>\frac{1}{3}(x)+3$ and $3x-y>2$.

Step-by-step explanation:

From the given given graph it is clear that the red line passing through the point (0,3) and (-3,2). The black line passing through the points (0,-2) and (1,1).

If a line passing through two points, then the equation of line is

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

The related equation of red line is

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

$y-3=\frac{1}{3}(x)$

$y=\frac{1}{3}(x)+3$

The red line is dotted and shaded potion is upper side of the line, therefore the sign of inequality is >.

$y>\frac{1}{3}(x)+3$          .... (1)

The related equation of black line is

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

$y+2=3x$

The black line is dotted and shaded potion is lower side of the line, therefore the sign of inequality is <.

$y+2$

$2$

$3x-y>2$          .... (2)

Therefore the graph represent the system of linear inequalities $y>\frac{1}{3}(x)+3$ and $3x-y>2$.

Answer 2

Im not good in math and this is my first question, my best guess is D

I will investigate tommorow this problem a little bit more... <3