A graph can be used to represent a system of inequality.
The system of inequality, the graph represents is:
[tex]y \ge 1[/tex] and [tex]y - x > 0[/tex]
The attached graph has two lines.
- A thick horizontal line
- A dotted slant line
The thick horizontal line
Below this line, is a shaded region; and it passed through [tex]y = 1.[/tex]
This means that the horizontal line represents all values of y starting from 1.
So, the inequality is:
[tex]y \ge 1[/tex]
A dotted slanted line
First, calculate the slope of the line
[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]
The line passes through (0,0) and (1,1).
So, we have:
[tex]m =\frac{1-0}{1-0}[/tex]
[tex]m =1[/tex]
The equation is:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 1(x - 0) + 0[/tex]
[tex]y = x + 0[/tex]
[tex]y = x[/tex]
The left part of the dotted line is shaded. This represents >.
So, we have:
[tex]y> x[/tex]
Subtract x from both sides
[tex]y - x > 0[/tex]
Hence, the system of inequality, the graph represents is:
[tex]y \ge 1[/tex]
[tex]y - x > 0[/tex]
Read more about system of inequalities at:
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