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Introduce the Coordinate plane, the 11 parts of it, how to name coordinates and plot points.

Objective. Introduce the Coordinate plane, the 11 parts of it, how to name coordinates and plot points. y-axis.

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Introduce the Coordinate plane, the 11 parts of it, how to name coordinates and plot points.

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  1. Objective Introduce the Coordinate plane, the 11 parts of it, how to name coordinates and plot points.

  2. y-axis The coordinate plane is formed by the intersection of two perpendicular number lines called axes. The point of intersection, called the origin, is at 0 on each number line. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis. ORIGIN x-axis

  3. The coordinate plane sectioned into 4 Quadrants. Starting in the upper right hand side, they are labeled Quadrant I, II, III, IV. Quadrant II Quadrant I (-,+) (+,+) All the points in each Quadrant have something in common. How they are feeling in the morning and evening! They are either Happy (+) or Sad (-) (-,-) (+,-) Quadrant III Quadrant IV

  4. Reading Math The x-coordinate tells how many units to move left or right from the origin. The y-coordinate tells how many units to move up or down. Think about going to a PARTY! Points on the coordinate plane are described using ordered pairs. An ordered pair consists of an x-coordinate and a y-coordinate and is written (x, y). ( x , y ) ( , )

  5. U(0, –5) • Example 1: Graphing Points in the Coordinate Plane Graph each point. A. T(–4, 4) Start at the origin. T(–4, 4) • Move 4 units left and 4 units up. B. U(0, –5) Start at the origin. Move 5 units down. • C. V (–2, –3) V(–2, −3) Start at the origin. Move 2 units left and 3 units down.

  6. Check It Out! Example 1 Graph each point. A. R(2, –3) Start at the origin. Move 2 units right and 3 units down. B. S(0, 2) Start at the origin. Move 2 units up. C. T(–2, 6) Start at the origin. Move 2 units left and 6 units up.

  7. Look at the graph at the top of this lesson. The axes divide the coordinate plane into four quadrants. Points that lie on an axis are not in any quadrant.

  8. •F •E •G •H Example 2: Locating Points in the Coordinate Plane Name the quadrant in which each point lies. y A. E Quadrant ll B. F no quadrant (y-axis) x C.G Quadrant l D.H Quadrant lll

  9. Check It Out! Example 2 Name the quadrant in which each point lies. y A. T •U •W no quadrant (y-axis) •T B. U Quadrant l x C.V Quadrant lll •V D.W Quadrant ll

  10. Lesson Quiz: Part 1 Graph each point. Name the quadrant in which each point lies. 1. (2, 0) None 2. (–3, –4) lll • 3. (1, –1) lV • • 4. (–5, 4) ll •

  11. When you graph ordered pairs generated by a function, they may create a pattern.

  12. • • • • • Example 4A: Generating and Graphing Ordered Pairs Generate ordered pairs for the function using the given values for x. Graph the ordered pairs and describe the pattern. y = 2x + 1; x = –2, –1, 0, 1, 2 (–2, –3) –2 2(–2)+ 1 = –3 2(–1)+ 1 = –1 (–1, –1) –1 2(0)+ 1 = 1 (0, 1) 0 2(1) + 1 = 3 1 (1, 3) 2(2) + 1 = 5 (2, 5) 2 The points form a line.

  13. Example 4B: Generating and Graphing Ordered Pairs y = x2– 3; x = –2, –1, 0, 1, 2 (–2, 1) –2 (–2)2– 3 = 1 (–1)2– 3 = –2 –1 (–1, –2) (0)2– 3 = –3 (0, –3) 0 (1)2– 3 = –2 1 (1, –2) (2)2– 3 = 1 (2, 1) 2 The points form a U shape.

  14. Example 4C: Generating and Graphing Ordered Pairs y = |x –2|; x = 0, 1, 2, 3, 4 0 (0, 2) |0– 2| = 2 |1– 2| = 1 1 (1, 1) |2– 2| = 0 (2, 0) 2 |3– 2| = 1 3 (3, 1) (4, 2) 4 |4– 2| = 2 The points form a V shape.

  15. 1 2 Check It Out! Example 4a y = x – 4; x = –4, –2, 0, 2, 4 (–4, –6) –4 –2 – 4 = –6 –2 –1 – 4 = –5 (–2, –5) 0 – 4 = –4 (0, –4) 0 1 – 4 = –3 2 (2, –3) 4 2 – 4 = –2 (4, –2) The points form a line.

  16. Check It Out! Example 4b y = 3x2 + 3; x = –3, –1, 0, 1, 3 (–3, 30) –3 3(–3)2+ 3 = 30 3(–1)2+ 3 = 6 –1 (–1, 6) 3(0)2+ 3 = 3 (0, 3) 0 3(1)2+ 3 = 6 1 (1, 6) 3(3)2+ 3 = 30 (3, 30) 3 The points form a U shape.

  17. Check It Out! Example 4c y = |x– 2|; x = 0, 1, 2, 3, 4 0 (0, 2) |0– 2| = 2 |1– 2| = 1 1 (1, 1) |2– 2| = 0 (2, 0) 2 |3– 2| = 1 3 (3, 1) (4, 2) 4 |4– 2| = 2 The points form a V shape.

  18. • • • • • Lesson Quiz: Part 3 6. Generate ordered pairs for y = x² –5 using x = –2, –1, 0, 1, and 2. Graph the ordered pairs, and describe the pattern. (–2, –1) (–1, –4) (0, –5) (1, –4) (2, –1) The pattern is U-shaped.

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