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The equation y = −2x + 3 is the boundary line for the inequality y ≤ −2x + 3. Which sentence describes the graph of the inequality?

A. The region shaded above a dashed boundary line.


B. The region shaded above a solid boundary line.


C. The region shaded below a solid boundary line.


D. The region shaded below a dashed boundary line.

Respuesta :

luisejr77

Answer: Option C

Step-by-step explanation:

The point-slope form of the equation of the line is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the intersection with the y-axis.

In the line [tex]y=-2x + 3[/tex], you can identify that:

[tex]m=-2\\b=3[/tex]

The symbol of the inequality "[tex]\leq[/tex]" indicates that you must shade the region below the boundary line and for the symbols of inequalities "[tex]\leq[/tex]" and "[tex]\geq[/tex]" the line must be solid (Observe the graph attached).

Then the answer is the option C.

Ver imagen luisejr77
kudzordzifrancis

Answer:

C. The region shaded below a solid boundary line.

Step-by-step explanation:

The given inequality is

[tex]y\le-2x+3[/tex]

The boundary line for this inequality is [tex]y=-2x+3[/tex].

Since the inequality involve [tex]\le[/tex], we use a solid boundary line.

After graphing the boundary line; we test the origin to determine which half -plane to be shaded. This is because the boundary lie is not passing through the origin.

Testing the origin yields [tex]0\le-2(0)+3[/tex].

This implies that;  [tex]0\le3[/tex]. This statement is true.

Hence we shade the lower half-plane of the solid boundary line.

The correct choice is C.

See graph

Ver imagen kudzordzifrancis

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