3-2

1. 3-2 Graphing on a Coordinate Plane Warm Up Problem of the Day Lesson Presentation Course 3

2. Warm Up Find the values for y by substituting 1, 3, 5, and 7 for x. 1.y = 2x  3 1, 3, 7, 11 2.y = 4x + 1 5, 13, 21, 29 3.y = 5x  5 0, 10, 20, 30

3. Problem of the Day What day is four days after the day before Saturday? Monday

4. Learn to graph points and lines on the coordinate plane.

5. Vocabulary coordinate plane x-axis y-axis quadrant x-coordinate y-coordinate origin graph of an equation

6. The coordinate plane is formed by two number lines, the x-axis and the y-axis. They intersect at right angles and divide the plane into four quadrants. The x-coordinate is the first number in an ordered pair. The y-coordinate is the second number in an ordered pair.

7. To plot an ordered pair, begin at the origin, the point (0, 0). It is the intersection of the x-axis and the y-axis. The x-coordinate tells how many units to move left or right; the y-coordinate tells how many units to move up or down.

8. (2, 3) (0, 0) y x Helpful Hint The sign of a number indicates which direction to move. Positive: up or right Negative: down or left Quadrant I Quadrant II move up 3 units move right 2 units (2, 3) origin Quadrant IV Quadrant III

9. y x Additional Example 1: Finding the Coordinates and Quadrants of Points on a Plane Give the coordinates and quadrants of each point. (1, 3); Quadrant l Point R is ________________ 1 unit right, 3 units up R (0, –3); no quadrant T Point S is _________________ 0 units right, 3 units down (–2, 2); Quadrant ll U Point T is _________________ 2 units left, 2 units up S (–3, 0); no quadrant Point U is ________________ 3 units left, 0 units up

10. y x Check It Out: Example 1 Give the coordinates and quadrants of each point. (0, 2); no quadrant Point J is __________________ K 0 units right, 2 units up (2, 0); no quadrant J Point M is _________________ 2 units right, 0 units up M (–1, 4); Quadrant ll Point K is __________________ P 1 unit left, 4 units up (–3, –2); Quadrant lll Point P is _________________ 3 units left, 2 units down

11. y C A x B D Additional Example 2: Graphing Points on a Coordinate Plane Graph each point on the coordinate plane. B. B(4, 0) A. A(3, 4) right 4, up 0 right 3, up 4 C. C(–4, 4) D. D(–1, –3) left 4, up 4 left 1, down 3

12. y C A x B D Check It Out: Example 2 Graph each point on the coordinate plane. B. B(2, 0) A. A(2, 4) right 2, up 0 right 2, up 4 C. C(–2, 4) D. D(–1, –1) left 2, up 4 left 1, down 1

13. The graph of an equation is the set of all ordered pairs that are solutions of the equation.

14. Additional Example 3: Graphing an Equation Complete the table y = 2x - 3. Graph the ordered pairs on a coordinate plane and draw a line through them. y x 2x – 3 y (x, y) 2(0) – 3 0 –3 (0, –3) x 1 2(1) – 3 –1 (1, –1) 2 2(2) – 3 1 (2, 1) 3 2(3) – 3 3 (3, 3)

15. Check It Out: Example 3 Complete the table y = 3x - 4. Graph the ordered pairs on a coordinate plane and draw a line through them. y x 3x – 4 y (x, y) 3(0) – 4 0 –4 (0, –4) x 1 3(1) – 4 –1 (1, –1) 2 3(2) – 4 2 (2, 2) 3 3(3) – 4 5 (3, 5)

16. y D B A x C Lesson Quiz: Part 1 Give the coordinates and quadrant of each point. 1. A 2.B Graph each point on the given coordinate plane. Label points C, D. 3. C (5, –2) 4. D (0, 4) (2, 0); none (3, 4); Quadrant ll

17. (2, 5) 4(0)  3 3 (0, 3) (1, 1) 4(1)  3 1 (1, 1) 4(2)  3 5 (2, 5) (0, 3) Lesson Quiz: Part 2 5. Complete the table for y = 4x – 3. Graph each ordered pair on the coordinate plane. y x