Download presentation

Presentation is loading. Please wait.

Published byLorin Horton Modified over 8 years ago

1
Graphing Linear Inequalities in Two Variables Section 6.5 Algebra I

2
Definitions Linear inequality: A linear inequality in x and y is an inequality that can be written as follows Solution: An ordered pair (x,y) is a solution of a linear inequality if the inequality is true when the values of x and y are substituted into the inequality

3
Example 1 Check whether the ordered pair is a solution of 2x-3y>-2 (0,0) (0,1) (2,-1)

4
Example 1 Continued For (0,0) both x and y are 0. Substitute 0 for x and 0 for y 2(0)-3(0) > -2 0-0 > -2 0 > -2 Since 0 is greater than -2, then (0,0) is a solution to the inequality

5
Example 1 continued To check if (0,1) is a solution, we use x=0 and y=1 2(0)-3(1) > -2 0-3 > -2 -3>-2 Since -3 is not greater than -2, then (0,1) is not a solution

6
Example 1 continued You check if (2,-1) is a solution

7
Definitions Graph: The graph of a linear inequality in two variables is the graph of the solutions of the inequality Half-plane: In a coordinate plane, the region on either side of a boundary line.

8
Example 2 Sketch a graph of y>-3 To do this, we will expand on our graphs from before. We are going to use a coordinate plane rather than a number line Use a dotted line for less than or greater than Use a solid line for less than or equal to and greater than or equal to

9
Example 2 continued Start by graphing y=-3

10
Example 2 continued Next, we need to shade in all values where y>-3

11
Example 3 Try to sketch the graph of x≤5. Remember, start with x=5. Is this a solid or dotted line? Then shade in where x≤5.

12
Example 3 continued

13
Did you get this?

14
Example 4 If you are given x-3>5…. How would you graph this? First, solve for x. x>8 Then graph as we did in the previous two examples.

15
Example 5 Sketch the graph of x – y < 2. First, graph the line x – y = 2. We would solve for y… -y = -x + 2 y = x – 2. Now, we know the slope is one and the y- intercept is -2. We also will graph using a dotted line.

16
Example 5 Continued

17
Example 5 continued To decide where to share, we can test a point on one side of the line. I like to test (0,0) if possible. For x – y < 2….. We can use x = 0, y = 0. 0 – 0 < 2 0 < 2 Since this is a true statement, we shade where (0,0) is at on the graph – as well as that side of the graph.

18
Example 5 Continued

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google