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Understanding Graphs and Linear Equations: A Comprehensive Review

This review covers the fundamentals of graphing linear equations and understanding ordered pairs within the coordinate plane. It includes identifying coordinates, determining which quadrant they belong to, and assessing solutions of equations through substitution. Students will learn to graph equations using ordered pairs and by creating tables. The material is designed to solidify comprehension of basic graphing concepts and linear equations, providing step-by-step guidance to find solutions and plot points accurately.

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Understanding Graphs and Linear Equations: A Comprehensive Review

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  1. Ch 7 Graphs and Linear Equations Review on Graphing

  2. y “origin” (0,0) Ordered Pair (x, y) x Coordinate Plane

  3. y “origin” (0,0) Ordered Pair (5, 4) x Coordinate Plane

  4. y “origin” (0,0) Ordered Pair (5, -4) x Coordinate Plane

  5. y Ordered Pair (-5, -4) x Coordinate Plane

  6. y Coordinates Ordered Pair (-5, 0) x (-5,0)

  7. y (0,6) Graph (0, 6) I II second quadrant first quadrant x III IV third quadrant fourth quadrant quadrants Not in a quadrant if on either axis

  8. y What are the coordinates? Which quadrant? I (1,1) x

  9. y What are the coordinates? Which quadrant? II (-3, 3) x

  10. y What are the coordinates? Which quadrant? x IV (5, -2)

  11. y What are the coordinates? Which quadrant? x (0, -5) Not in a quadrant if on either axis

  12. 7.2 Graphing Equations Objectives: • Learn to determine if an ordered pair is a solution of an equation. • Graph equations using ordered pairs.

  13. How do you determine if an ordered pair is a solution?? You plug in the (x, y) value into your x and y in the equations and see if the right side = the left

  14. Determine if the ordered pair is a solution of the equation. y = 2x + 1 (3 ,7 ) 7 = 2(3) + 1 YES The ordered pair (3,7) is a solution.

  15. Determine if the ordered pair is a solution of the equation. 4y - 3x = 22 (-2 ,4 ) 4(4) – 3 (-2)= 22 16 + 6 = 22 YES The ordered pair (-2,4) is a solution.

  16. Determine if the ordered pair is a solution of the equation. y - 3x = -2 (-2 ,8 ) (8) – 3 (-2)= -2 ??? 8 + 6  -2 NO The ordered pair (-2,8) is not a solution.

  17. Graphing Equations • We are going to learn three ways to graph a linear equation. Today we are going to learn how to graph by “Making a Table”

  18. Making a Table • Solve the equation in y = format (slope intercept form) • Pick your x values (-1, 0,1) • Plug in the x values into x in the equation to find the corresponding y values • Plot the (x, y) ordered pairs on the coordinate plane

  19. y x y Graph: y = x x

  20. y Find 3 solutions y = 2x + 1 x 1 3 (1,3) 2(1) +1 1 0 2(0) +1 (0,1) -1 2(-1) +1 (-1,-1) -1

  21. Solve for ‘y’ Solve for ‘y’ means “get y all by itself”

  22. y Graph: -2x + y = 5 y = 2x + 5 x 1 2(1) +5 7 (1,7) 0 2(0) +5 5 (0,5) -1 2(-1)+5 3 (-1,3)

  23. y Graph: -2x + 3y = 15 3y = 2x + 15 x Y=2/3x +5 3 7 (3,7) (2/3)(3) +5 0 5 (2/3) (0) +5 (0,5) -3 3 (2/3)(-3)+5 (-3,3)

  24. y x y Graph: 3x - y = 2 3x = y + 2 3x - 2 = y x

  25. Assignment:Page 311(2-26) even-Use graph paper- #’s 8-14 just make the table you do not have to graph-#’s 16-26 make the table and graph

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