Question

What system of inequalities is represented by the graph?

Please answer as fast as you can, I’m in a test.
(The lines continue out with no points that all the inequalities)

Answer 1

The system of inequalities represented by the graph is y ≥ x - 2, y < -3x - 6

What system of inequalities is represented by the graph?

From the question, we have the following parameters that can be used in our computation:

The graph

A linear equation is represented as

y = mx + c

Where

c = y-intercept i.e. c = y, when = 0

Considering the dotted lines, we have the following points

(0, -6) and (-2, 0)

So, e have

y = mx - 6

Using the point (-2, 0), we have

-2m - 6 = 0

m = -3

So, we have

y = -3x - 6

The inequality is a dotted line, shaded to the left

So, we have

y < -3x - 6

Considering the closed lines, we have the following points

(0, -2) and (-4, -6)

So, e have

y = mx - 2

Using the point (-4, -6), we have

-4m - 2 = -6

-4m = -4

m = 1

So, we have

y = x - 2

The inequality is a closed line, shaded to the right

So, we have

y ≥ x - 2

Hence, the system of inequalities is y ≥ x - 2, y < -3x - 6