Question

Choose the system for the graph.

Answer 1

Answer:

$\textsf{D.} \quad \begin{cases} y \leq 2x+2 \\ y\geq -\dfrac{1}{2}x \end{cases}$

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:

$\textsf{D.} \quad \begin{cases} y \leq 2x+2 \\ y\geq -\dfrac{1}{2}x \end{cases}$

Learn more about graphing inequalities here:

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