Sec. 9.1 Linear Inequalities in Two Variables
Chapter 9: Linear and Quadratic Inequalities
9.1 Linear Inequalities
Linear Equation
Linear Inequality
Graph 4x + 2y = 10
Graph 4x + 2y ≤ 10
Each (x,y) pair on the line is
a solution to the equation.
Each (x, y) pair _______________
the line is a solution to the inequality.
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In general, to graph an inequality:
1) Graph the boundary line. (change to slope-intercept form)
2) Draw a solid line if the inequality is ≥ or ≤ (The points on the line are included)
Draw a dashed line if the inequality is > or < (The points on the line are not included)
3) Test a point not on the boundary line.
→ If the point makes the inequality true, shade that side of the line.
→ If the point does not make the inequality true, shade the opposite side of the line.
The point (0, 0) makes a good test point.
Ex. 2 Graph
Graph boundary line. Solid or Dashed ?
Determine Region to be shaded.
Ex. 3
a) Given the graph, determine the equation.
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b) Which points satisfy the inequality?
Ex. 4 A mosaic is made of tile and stone. The budget for the mosaic is $180. If the tile costs $4.00/ft2
and the stone costs $4.50/kg, draw a graph to represent all possible combinations of stone and tile that can be
used to create the mosaic.
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Ex. 5 A smart phone plan (Plan A) charges 10 cents/min and 10 cents for each megabyte of data. Another plan
(Plan B) allows unlimited talk and data for $50/month. Under what circumstances is Plan A better?
Assignment: Sec. 9.1 p. 472 # 1-2ac, 3ace, 4, 6, 9, 11-13, 15
Final Exam is coming up!!!
Block D - Monday, June 15th 12:30-2:30
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