Download presentation

Presentation is loading. Please wait.

Published byMargery Daisy Tyler Modified over 7 years ago

1
Linear Inequalities Page 178

2
Formulas of Lines Slope Formula Slope Intercept Form Point Slope Form Ax + By = C Standard Form A,B,C ∈ℤ, A ≥ 0 Ax + By + C = 0 General Form a a a

3
Slopes of Parallel Lines Parallel lines have the same slope. If they are both in slope-intercept form then only the y-intercept is different. Examples y=2x+6y-3=4(x+1) y=2x-8y+2=4(x+9)

4
Slopes of Perpendicular Lines Perpendicular lines have slopes which are opposite reciprocals of each other. y=2x -2 is perpendicular to all lines y= -½ x + b for all values of b The product of the slopes of perpendicular lines is -1. 2 - ½ = -1

5
A linear inequality in 2 variables is a graph that is half of the coordinate plane. Draw the solid or dotted line and shade on one side of it. Linear Inequalities

6
< Is less than > is greater than ≥ is greater than or equal to ≤ is less than or equal to ≠ is not equal to or ≠ dotted line ≤ or ≥ solid line

7
A solution of an inequality in two variables, x and y, is an ordered pair of real numbers with the following property: When the coordinates are substituted into the inequality, we obtain a true statement. Every ordered pair that is part of the solution “satisfies” the inequality.

8
Determining if an ordered pair is a solution Substitute the ordered pair into both inequalities and see if the solutions are true. If both are true, the ordered pair is a solution. if the ordered pair gives a false solution in either equation, the ordered pair does not satisfy the system of inequalities. Is (3,1) a solution to the system of inequalities? y<2x-2 and y≥x-1

9
How to graph A linear inequality is a region of a plane with a boundary line. The solutions of an inequality are all the points that make the inequality true and are represented by a shaded part of the graph. 1)Graph it like an equation by plotting points and determine how to connect the points with a solid or dotted line. 2)Then determine where to shade!

10
Where do we shade?? If the equation is in slope intercept form with y on one side and everything else on the other, y> or y≥ shades above the line and y< and y≤ shade below the line. If you are not sure, pick a point not on the line and substitute it to see if it is a solution or not. If it is a solution shade there, if not, shade the other side.

11
A linear inequality is a region of a plane with a boundary line. The solutions of an inequality are all the points that make the inequality true and are represented by a shaded part of the graph. y>5x+2 noticed the dotted line

12
y≤2x+1 Notice the solid line

13
y>4x-1 pick any point like (0,0) if it is true, shade on the left, if it is false, shade on the right where (0,0) is located).

14
y>4x-1 pick a point (0,0) if it is true, shade on the left, false, shade on the right where (0,0) is located. 0>4(0)-1 0>-1 true

15
(a) (b) (c) (d)

16
Graphing > or < graph with a dotted line ≥ or ≤ graph with a solid line Then determine where to shade. Pick a test point and if the inequality is true for the test point, graph that side of the line.

17
y<4x-1

18
y≥-4x-3

19
(a) (b) (c) (d)

20
Practice Pages 180-181

21
1)y > 0.5x – 4 (0,0), (8,2) are solutions (2, -4) 2)2x – 3y ≤ 10 (9,3) is a solution (3,-2),(-5,-7) 3) 4)

22
Classwork/ 나우웤 열람실웤 /Homework page 183 - 187

Similar presentations

© 2023 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