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Choose the system for the graph.
y 2 2x+2
y2-x
A.
B.
C.
D.
≤ 2x - 1
yz -x + 2
y≤-2x + 2
(y 2 x
ys 2x + 2
y >- 1x


Choose The System For The Graph Y 2 2x2 Y2x A B C D 2x 1 Yz X 2 Y2x 2 Y 2 X Ys 2x 2 Y Gt 1x class=

Sagot :

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]

Learn more about graphing inequalities here:

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