Graph linear inequalities in two variables

1. Graph linear inequalities in two variables Section 6.7

2. Concept • Up until this point we’ve discussed inequalities that involve only one dimension or one variable • Today we’re going to take our understanding of inequalities and apply it to two dimensions (variables) • First we will do a short review of lines and linear terms

3. Slope • Slope is • A. An index of the angle of a line • B. A ratio of how much a line increases versus how much to moves right of left • C. A ratio of run to rise • D. An index of movement in the x direction

4. Slope • What is the slope of the line that goes through the points (1,2) & (5,4)

5. Slope • What is the slope of the line that goes through the points (-4,-2) & (7,-8)

6. Slope • What is the slope of the line that goes through the points &

7. Slope • What is the slope of the line that goes through the points (5,2) & (5,4)

8. Slope • What is the equation of the line that goes through the points (1,3) & (3,7)

9. Slope • What is the equation of the line that goes through the points (-3,4) & (-5,-12)

10. Slope • What is the equation of the vertical line that goes through the point (3,-5)

11. Slope • The equation of a line is y=3x-9. The slope of the line is increased by 2. What happens to the line? • A. The line has the same y-intercept, but now slopes downward • B. The line has the same y-intercept, but is now steeper • C. The line has a different y-intercept, but now slopes downward • D. The line has a different y-intercept, but is now steeper

12. Slope • Assuming that the line starts at x=0, which line will reach y=50 first?

13. The big idea Y X • When we look at a line, we’re seeing the collection of points that are solutions to a linear equality • When looking at a linear inequality, instead of looking at a set of points, we are seeing a defined space that indicates the infinite collection of points that satisfy the criteria • For example This means that any point that falls in the shaded area is a viable solution to the inequality

14. Testing a point Y X • We can see this by testing out a point in the shaded area • For example It’s imperative that we remember that the solution to these inequalities is an area as opposed to a line (-6,3)

15. Process out of examples Y X • Our process for creating these graphs is not difficult, but rather just an extension of our previous knowledge of graphing Graph the line via linear graphing methods Draw a dashed line for >,< otherwise a solid line Shade the appropriate area Above for greater than Below for less than

16. Example Y X • Let’s do an example

17. Example Y X • How would we graph this one?

18. Example Y X • We would operate horizontal and vertical inequalities the same as any other inequality

19. Examples Y X

20. Example Y X • And another one

21. Example Y X • And another one

22. Practical Example Y X • A party shop makes giftbags for birthday parties. They charge $4 per glowstick and $10 per T-shirt. Let x represent the number of glowsticks and y the number of T-shirts. The goal is to earn at least $500 from the sale of the bags • Write an inequality that • describes the goal in • terms of x & y • Graph the inequality • Give three possible • combinations of pairs • that will allow the shop • to meet it’s goal

23. Most Important Points • What’s the most important thing that we can learn from today? • The solution to an inequality in two-dimensions is an area, as opposed to a line • We can graph the solutions to an equation by following our normal processes for graphing lines and then shading the appropriate area

24. Homework 6.7 you will have two days 1, 2-32, 47-50, 53-57