Questions: Correct the set of the following linear inequality: y + 4 < -x Choose the type of boundary line: Solid (-) Dashed ( -- -) Enter two points on the boundary line: Select the region you wish to be shaded: A B

Correct the set of the following linear inequality:
y + 4 < -x

Choose the type of boundary line:
Solid (-) Dashed ( -- -)

Enter two points on the boundary line:

Select the region you wish to be shaded:

A B

Transcript text: 4.6 Graphing Linear Inequalities Lesson: 4.6 Graphing Linear Inequalities Correct the set of the following linear inequality: \[ y+4<-x \] Choose the type of boundary line: Solid $(-)$ Dashed ( -- -) Enter two points on the boundary line: Select the region you wish to be shaded: A B

Solution

Solution Steps

Step 1: Rewrite the Inequality in Slope-Intercept Form

The given inequality is $ y + 4 < -x $. To rewrite it in slope-intercept form ($ y = mx + b $), solve for $ y $: \[ y < -x - 4 \]

Step 2: Determine the Boundary Line

The boundary line for the inequality $ y < -x - 4 $ is $ y = -x - 4 $. Since the inequality is strict (less than), the boundary line will be dashed.

Step 3: Plot the Boundary Line

To plot the boundary line $ y = -x - 4 $, find two points on the line:

When $ x = 0 $, $ y = -4 $. So, one point is (0, -4).
When $ x = -4 $, $ y = 0 $. So, another point is (-4, 0).

Plot these points on the graph and draw a dashed line through them.

Step 4: Determine the Shaded Region

Since the inequality is $ y < -x - 4 $, shade the region below the dashed line. This is the region where the y-values are less than those on the line.