System of Inequalities

The graph of a system of inequalities is shown.

Create the system of inequalities that is represented by the graph.

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Determine the boundary line of each of the two inequalities first.

It is necessary to determine the y-intercept, slope, and inequality sign of each boundary line.
A dashed boundary line designates using a < or > sign.
A solid boundary line designates a ≤ or ≥ sign.
An inequality shaded above the line uses a > or ≥ sign.
An inequality shaded below the boundary line uses a < or ≤ sign.

Slope-intercept form is y = mx + b
m is the slope of the line
b is the y-intercept of the line

One line has a y-intercept of -3 and a slope of 0, with a dashed boundary line.  Also it is shaded below the line, indicating
the use of a < sign.
y < -3   {slope is zero and the y-intercept is -3}

The other line has a y-intercept of -5 and a slope of 2/3.  Also, it is shaded above the line, indicating the use of a ≥ sign
y ≥ (2/3)x - 5   {slope is 2/3 and the y-intercept is -5}

The system of inequalities is:
y < -3
y ≥ (2/3)x - 5


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