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

C. The region shaded below a solid boundary line.

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

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.