Question

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.

Answer 1

Answer:

C. The region shaded below a solid boundary line.

Step-by-step explanation:

The given inequality is

$y\le-2x+3$

The boundary line for this inequality is $y=-2x+3$.

Since the inequality involve $\le$, 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 $0\le-2(0)+3$.

This implies that;  $0\le3$. This statement is true.

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

The correct choice is C.

See graph

Answer 2

Answer: Option C

Step-by-step explanation:

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

$y=mx+b$

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

In the line $y=-2x + 3$, you can identify that:

$m=-2\\b=3$

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

Then the answer is the option C.