1 / 29

Solving Equations & Inequalities: Graphing and Geometric Transformations

Learn how to solve equations and inequalities by combining like terms, eliminating constants and coefficients, and graphing. Also, explore geometric transformations like translation, reflection, rotation, and dilation.

donnyj
Download Presentation

Solving Equations & Inequalities: Graphing and Geometric Transformations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SOLVING EQUATIONS!!! 1. Combine "Like" terms. 2. Get rid of your Constant. 3. Get rid of your Coefficient. Do the opposite of what the problem is telling you to do. x + 4 + x - 5 = 19

  2. Graphing Equations y = mx + b Slope Rise/Run Y-intercept -4x + 2y = 10

  3. SOLVING INEQUALITIES!!! 1. Combine "Like" terms. 2. Get rid of your Constant. 3. Get rid of your Coefficient. Do the opposite of what the problem is telling you to do. **When Multiplying or Dividing a negative "across the inequality," flip your sign. -3x + 4 - 2x + 3 > 27

  4. Graphing Inequalities Proper Point Arrow Trick

  5. Systems of Equations

  6. Solution to a System

  7. Linear Equations with No Solution STEP 1: Graph both lines. STEP 2: Find the intersection. STEP 3: Check to see if the ordered pair of the intersection makes both equations TRUE.

  8. Linear Equations with Infinitely Many Solutions Solve the linear system: 2x + y = 4 EQUATION 1 -6x - 3y = -12 EQUATION 2

  9. Systems of Equations through Substitution When you have two equations with the same set of variables, if you can figure out what one variable is, you can use it to find the other. 2y = 20 + 20x y = 5x

  10. Systems of Inequalities Review at the end if there is time.

  11. Geometric Transformations or "Moving Stuff with Math"

  12. Translation Rules: When moving left, subtract from your X. When moving right, add to your X. When moving down, subtract from your Y. When moving up, add to your Y.

  13. Translating Shapes 1 Translate Triangle A five units right and three units down. (-4,5) A (-2,-2) (-6,-2)

  14. Rules for Reflection: When you are flipping across the X axis, change the sign of your Y. When you are flipping across the Y axis, change the sign of your X. When you are flipping across Y = X,flip your X and Y. When you are flipping across Y = -X. flip your X and Y and change their signs.

  15. Reflecting Shapes Reflect the square across the y-axis. A B C D (-8,7) (-8,4) (-5,7) (-5,4)

  16. Rotation Rules: 90 degrees rotation clockwise. (x,y) → (y,-x) 180 degrees rotation. (x,y) → (-x, -y) 90 degrees rotation counterclockwise (also clockwise 270) (x,y) → (-y, x)

  17. Rotate the following shape 90° clockwise about the origin. A(-8,-2) B(-6,-2) C(-8,-6) A(-8,-2) B(-6,-2) D(-6,-6) C(-8,-6) D(-6,-6)

  18. Dilation Rules: Scale Factor: k k > 1 0 < k < 1 k = 1 Dilated image is larger than preimage. Dilated image is smaller than preimage. No change. Same size as preimage. (Any Numbers greater than 1) (Fractions less than 1)

  19. Dilating a shape. 1 __ (x,y) (x,y) A C 2 A(2,8) A'(__,__) D B B(2,2) B'(__,__) C(5,8) C'(__,__) D(5,2) D'(__,__)

  20. Pythagorean Theorem a² + b² = c²

  21. What is the missing side length? x 4 3

  22. Questions about specific skills?

  23. Graphing Linear Inequalities STEP 1: Find the equation of the boundary line by replacing the inequality symbol with =. Graph this equation. Use a dashed line for < or >. Use a solid line for ≤ or ≥.

  24. Graphing Linear Inequalities STEP 2: Test a point in one of the half-planes to determine whether it is a solution of the inequality. If the test point is a solution, shade the half-plane that contains the point. If not, shade the other half-point.

  25. Solving Systems of Linear Inequalities 1 y < -x - 2

  26. Systems of Linear Equations. Graph both Inequalities. Wherever they overlap, that is your "common solution."

  27. Solving Systems of Linear Inequalities 1

More Related