Objective: graph points and lines on the coordinate plane Chapter 1 Algebra Toolbox 1-8 Graphing on a Coordinate Plane Objective: graph points and lines on the coordinate plane

Agenda Warm Up Lesson Presentation Practice Activity Quiz

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

Learn to graph points and lines on the coordinate plane.

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

The coordinate plane is like a map formed by two number lines, the x-axis and the y-axis, that intersect at right angles. Ordered pairs are the locations, or points, on the map. The x-coordinate and y-coordinate of an ordered pair tell the direction and number of units to move. y-coordinate move up or down x-coordinate move right or left (x, y)

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

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

Finding the Coordinates of Points on a Plane Example 1: Finding the Coordinates of Points on a Plane Give the coordinates of each point. x y (1, 3) Point R is _______. 1 unit right, 3 units up R S T U (0, –4) Point S is _______. 0 units right, 4 units down (–2, 2) Point T is _______. 2 units left, 2 units up (–3, 0) Point U is _______. 3 units left, 0 units up

Give the coordinates of each point. Try This: Example 1 Give the coordinates of each point. x y (0, 2) Point J is _______. K 0 units right, 2 units up J (2, 0) Point M is _______. 2 units right, 0 units up M (–1, 4) Point K is _______. P 1 unit left, 4 units up (–3, –2) Point P is _______. 3 units left, 2 units down

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

Graph each point on the coordinate plane. Label the points A-D. Try This: Example 2 Graph each point on the coordinate plane. Label the points A-D. x y C A A. (2, 4) B. (2, 0) right 2, up 4 right 2, up 0 C. (–2, 4) 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.

Example 3A: Graphing an Equation Complete the table of ordered pairs. Graph the equation on a coordinate plane. x y A. y = 3x x 3x y (x, y) 3(0) (0, 0) 1 3(1) 3 (1, 3) 2 3(2) 6 (2, 6) 3 3(3) 9 (3, 9)

Example 3B: Graphing an Equation Complete the table of ordered pairs. Graph the equation on a coordinate plane. y B. y = 2x – 3 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)

Try This: Example 3A Complete the table of ordered pairs. Graph the equation on a coordinate plane. x y A. y = 2x x 2x y (x, y) 2(0) (0, 0) 1 2(1) 2 (1, 2) 2 2(2) 4 (2, 4) 3 2(3) 6 (3, 6)

Try This: Example 3B Complete each table of ordered pairs. Graph each equation on a coordinate plane. y B. y = 3x – 4 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 of each point. Lesson Quiz: Part 1 Give the coordinates 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) (3, 4) C

Complete the table. Graph the equation on the given coordinate plane. Lesson Quiz: Part 2 Complete the table. Graph the equation on the given coordinate plane. 5. y = 4x – 3 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)

Let’s try some!