Math  /  Geometry

QuestionGraph this inequality: y<13x3y<\frac{1}{3} x-3
Plot points on the boundary line. Select the line to switch between solid and dot region to shade it.

Studdy Solution

STEP 1

1. The inequality is linear.
2. The boundary line is y=13x3 y = \frac{1}{3}x - 3 .
3. The inequality is strict (<<), so the boundary line will be dashed.

STEP 2

1. Identify the boundary line.
2. Plot points on the boundary line.
3. Draw the boundary line.
4. Determine the region to shade.

STEP 3

Identify the boundary line from the inequality:
The boundary line is y=13x3 y = \frac{1}{3}x - 3 .

STEP 4

Plot points on the boundary line:
To find points, choose values for x x and solve for y y .
- Let x=0 x = 0 : $ y = \frac{1}{3}(0) - 3 = -3 \] Point: \( (0, -3) \)
- Let x=3 x = 3 : $ y = \frac{1}{3}(3) - 3 = 0 - 3 = -3 \] Point: \( (3, -2) \)
- Let x=6 x = 6 : $ y = \frac{1}{3}(6) - 3 = 2 - 3 = -1 \] Point: \( (6, -1) \)

STEP 5

Draw the boundary line:
- Plot the points (0,3) (0, -3) , (3,2) (3, -2) , and (6,1) (6, -1) . - Connect these points with a dashed line because the inequality is strict (<<).

STEP 6

Determine the region to shade:
- Since the inequality is y<13x3 y < \frac{1}{3}x - 3 , shade the region below the dashed line.
The graph of the inequality is complete with the dashed boundary line and the shaded region below it.

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