Questions: Graph this inequality: y < 1/3 x - 3 Plot points on the boundary line. Select the line to switch between solid and dotted. select a region to shade it.

Graph this inequality:
y < 1/3 x - 3

Plot points on the boundary line. Select the line to switch between solid and dotted. select a region to shade it.

Transcript text: Graph this inequality: \[ y<\frac{1}{3} x-3 \] Plot points on the boundary line. Select the line to switch between solid and dotted. select a region to shade it.

Solution

Solution Steps

Step 1: Find the boundary line

The inequality is y < (1/3)x - 3. The boundary line is y = (1/3)x - 3.

Step 2: Plot points on the boundary line

When x = 0, y = -3. When x = 3, y = -2. When x = 6, y = -1.

Step 3: Determine the line type

Since the inequality is y < (1/3)x - 3, the boundary line should be dotted.

Step 4: Determine the shaded region

Test the point (0,0): 0 < (1/3)(0) - 3 => 0 < -3, which is false. Shade the region that does _not_ include the point (0,0), i.e., the region below the line.