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Section 2.8 – Two variable Inequalities Essential Understanding
Graphing an inequality in two variables is similar to graphing a line. The graph of a linear
inequality contains all points on one side of the line and may or may not include the points on the
line.
Section 2.8 – Two variable Inequalities A linear inequality is an inequality in two variables
whose graph is a region of the coordinate plane bounded by a line.
This line is the boundary of the graph.
The boundary separates the coordinate plane into two half-planes, one of which consists of the solutions in the
inequality.
Section 2.8 – Two variable Inequalities To determine which half-plane to shade, pick a test point that is not on the boundary. Check whether than point satisfies the inequality. If it
does, shade the half-plane that includes the test point. If not, shade the other half-plane.
The origin (0,0) is usually the easiest test point as long as it is NOT on the boundary.
Section 2.8 – Two variable Inequalities Problem 1:
What is the graph of y > 3x – 1?
Section 2.8 – Two variable Inequalities Problem 1:
What is the graph of y < 3x – 1?
Section 2.8 – Two variable Inequalities Problem 1:
What is the graph of 2x + 3y > 12?
Section 2.8 – Two variable Inequalities Problem 1:
What is the graph of 5 – y > x
Section 2.8 – Two variable Inequalities Problem 2:
You need 5 tickets to ride a large ride and 3 tickets to ride a small ride at a local festival. You do not want to
spend more than $15 on tickets. The tickets are $0.25 a piece. How many small or large rides can you ride?
Section 2.8 – Two variable Inequalities Problem 3:
What is the graph of 1 – y < |x + 2|?
Section 2.8 – Two variable Inequalities Problem 3:
What is the graph of y – 4 > |x – 1| ?
Section 2.8 – Two variable Inequalities Problem 4:
What inequality goes this graph represent?
Section 2.8 – Two variable Inequalities Problem 4:
What inequality goes this graph represent?
Section 2.8 – Two variable Inequalities Problem 4:
What inequality goes this graph represent?
Section 2.8 – Two variable Inequalities Problem 5:
The graph at the right relates the amount of gas in the tank of your car to the distance you can drive.
a. Describe the domain for this situation.b. Why does the graph stop?c. Why is only the first quadrant shown?d. Why would every point in the region be a solution?e. Write an inequality for the graph.f. What does the coefficient of x represent?
Section 2.8 – Two variable Inequalities
