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

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

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

Learn to graph points and lines on the coordinate plane.

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

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.

To plot an ordered pair, begin at the origin, the point (0, 0) 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.

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

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

Give the coordinates and quadrants of each point. Check It Out: Example 1 Give the coordinates and quadrants of each point. x y (0, 2); no quadrant Point J is __________________ K 0 units right, 2 units up J (2, 0); no quadrant 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

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

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

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

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 –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)

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 –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)

Give the coordinates and quadrant of each point. 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) x y A B D (2, 0); none (3, 4); Quadrant ll C

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