Answer:
[tex]\textsf{D.} \quad \begin{cases} y \leq 2x+2 \\ y\geq -\dfrac{1}{2}x \end{cases}[/tex]
Step-by-step explanation:
Both lines in the given system of inequalities are linear equations.
Slope-intercept form of a linear equation: y = mx + b
(where m is the slope and b is the y-intercept)
Positive slope (m): as x increases, y increases.
Negative slope (-m): as x increases, y decreases.
When graphing inequalities:
- < or > : dashed lines
- ≤ or ≥ : solid line
- < or ≤ : shading under the line
- > or ≥ : shading above the line
The inequality represented by the blue line has a positive slope and shading below the line.
⇒ y ≤ mx + b
From inspection of the graph, its y-intercept is 2.
⇒ y ≤ mx + 2
The inequality represented by the yellow line has a negative slope and shading above the line.
⇒ y ≥ -mx + b
From inspection of the graph, it's y-intercept is zero.
⇒ y ≥ -mx
The only pair of inequalities that satisfies the above conditions is:
[tex]\textsf{D.} \quad \begin{cases} y \leq 2x+2 \\ y\geq -\dfrac{1}{2}x \end{cases}[/tex]
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