Graphing Linear Inequalities

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Show your work for each problem.

1.
What type of line do you use for ?
1. a)A curved line
2. b)No line needed
3. c)Dashed line (points on the line are NOT solutions)
4. d)Solid line (points on the line ARE solutions)
2.
What type of line do you use for ?
1. a)No line, just shading
2. b)A wavy line
3. c)Solid line (points on the line ARE solutions)
4. d)Dashed line (points on the line are NOT solutions)
3.
What is the slope of the boundary line for ?
4.
What is the y-intercept of the boundary line for ?
5.
For the inequality , is the point a solution?
1. a)Yes, because the origin is always a solution
2. b)Cannot determine without graphing
3. c)No, because is false
4. d)Yes, because is true
6.
Which region should be shaded for after testing ?
1. a)Both sides of the line
2. b)The side NOT containing because the test failed
3. c)Neither side, only the line
4. d)The side containing because the test passed
7.
Graph the inequality . Determine the boundary line, line type, and which side to shade.
8.
Convert to slope-intercept form. What is the y-intercept?
9.
Graph . Convert to slope-intercept form first, then determine line type and shading.
10.
The boundary line passes through the origin. Which test point should you use instead of ?
1. a)A point on the line itself
2. b) still works
3. c)No test point is needed
4. d) or - any point NOT on the line
11.
Graph completely. Note: the boundary passes through the origin.
12.
For the inequality , convert to slope-intercept form. What is the slope?
13.
A company has at most 500 dollars for supplies. Paper costs 5 dollars per ream and ink costs 25 dollars per cartridge. Which inequality represents this?
1. a)
2. b)
3. c)
4. d)
14.
You need to buy at least 12 notebooks. Large notebooks cost 8 dollars and small ones cost 4 dollars. Your budget is 60 dollars. Write an inequality for the budget constraint and test if 5 large and 4 small notebooks is affordable.
15.
What does the shaded region represent in a graph of a linear inequality?
1. a)Points that are NOT solutions
2. b)Only the points on the boundary line
3. c)The origin only
4. d)All the points that are solutions to the inequality