Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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? Tuesday

Learn to graph points and lines on the coordinate plane.

Vocabulary coordinate plane x-axis y-axis quadrant x-coordinate origin

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

Additional Example 3A: Finding Horizontal and Vertical Distances Find the distance between each pair of points. A. K and L y Use the x-coordinates. 10 8 M(2, 6)‏ Distance = |–2 – (4)| 6 4 = |–6| 2 x 8 6 4 2 2 4 6 8 = 6 2 L(4, –2)‏ K(–2, –2)‏ 4 The points are 6 units apart. 6 N(2, –6)‏ 8

The order of the points does not matter when you find the distance between them. Helpful Hint

Additional Example 3B: Finding Horizontal and Vertical Distances Find the distance between each pair of points. A. M and N y Use the y-coordinates. 10 8 M(2, 6)‏ Distance = |6 – (–6 )| 6 4 = |12| 2 x 8 6 4 2 2 4 6 8 = 12 2 L(4, –2)‏ K(–2, –2)‏ 4 The points are 12 units apart. 6 N(2, –6)‏ 8

Check It Out: Additional Example 3A Find the distance between each pair of points. A. A and B y Use the x-coordinates. 10 8 Distance = |–2 – (6)| A(–2, 4)‏ 6 B(6, 4)‏ 4 = |–8| 2 x 8 6 4 2 2 4 6 8 = 8 2 C(4, –2)‏ 4 The points are 8 units apart. 6 8 D(4, –8)‏

Check It Out: Additional Example 3B Find the distance between each pair of points. B. C and D y Use the y-coordinates. 10 8 Distance = |–2 – (–8)| A(–2, 4)‏ 6 B(6, 4)‏ 4 = |6| 2 x 8 6 4 2 2 4 6 8 = 6 2 C(4, –2)‏ 4 The points are 6 units apart. 6 8 D(4, –8)‏

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Give the coordinates and quadrant of each point. 1. A 2. C Lesson Quiz: Part I Give the coordinates and quadrant of each point. 1. A 2. C y (–8,–4), lll 10 (–4, 6), ll M 8 C Graph each point on a coordinate plane. 3. L(6, –8) 4. M(0, 8)‏ x –8 8 A B D –8 L

Find the distance between each pair of points on the graph above. Lesson Quiz: Part II Find the distance between each pair of points on the graph above. 5. A and B 6. C and D 14 units y 12 units M 8 C x –8 8 A B D –8 L

Lesson Quiz for Student Response Systems Identify the coordinates and quadrant of point A. A. (0, 3); none C. (3, 0); II B. (3, 0); I D. (0, 3); II

Lesson Quiz for Student Response Systems 2. Identify the coordinates and quadrant of point B. A. (3, –4); none C. (–4, 3); II B. (3, –4); I D. (–4, 3); IV

Lesson Quiz for Student Response Systems 3. Identify the graph of the point A(4, –3). C. D.

Lesson Quiz for Student Response Systems 4. Identify the graph of the point G(2, 0). C. D.

Lesson Quiz for Student Response Systems Identify the table for y = 3x – 4 and the graph of each ordered pair. B.