2-2 Graphing on a Coordinate Plane

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

2-2 Graphing on a Coordinate Plane

Warm UpFind the values for y by substituting 1, 3, 5, and 7 for x.

1, 3, 7, 115, 13, 21, 290, 10, 20, 303. y = 5x – 5

2. y = 4x + 11. y = 2x – 3

2-2 Graphing on a Coordinate Plane

Problem of the Day

What day is four days after the day before Saturday?

Tuesday

2-2 Graphing on a Coordinate Plane

Learn to graph points and lines on the coordinate plane.

2-2 Graphing on a Coordinate Plane

Vocabularycoordinate planex-axisy-axisquadrantx-coordinatey-coordinateorigin

2-2 Graphing on a Coordinate Plane

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.

2-2 Graphing on a Coordinate Plane

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.

2-2 Graphing on a Coordinate Plane

(2, 3)

The sign of a number indicates which direction to move. Positive: up or right Negative: down or left

Helpful Hint

x

y

origin

(2, 3)move right 2 units

move up 3 units

(0, 0)

Quadrant IQuadrant II

Quadrant III Quadrant IV

2-2 Graphing on a Coordinate Plane

Additional Example 1: Finding the Coordinates and Quadrants of Points on a Plane

Give the coordinates and quadrants of each point.

Point R is ________________(1, 3); Quadrant l

1 unit right, 3 units up

Point S is _________________(0, –3); no quadrant

0 units right, 3 units down

Point T is _________________(–2, 2); Quadrant ll

2 units left, 2 units up

Point U is ________________(–3, 0); no quadrant

3 units left, 0 units up

x

y

R

S

T

U

2-2 Graphing on a Coordinate Plane

Check It Out: Example 1

Point J is __________________(0, 2); no quadrant

0 units right, 2 units up

Point M is _________________(2, 0); no quadrant

2 units right, 0 units up

Point K is __________________(–1, 4); Quadrant ll

1 unit left, 4 units up

Point P is _________________(–3, –2); Quadrant lll

3 units left, 2 units down

x

y

J

P

K

M

Give the coordinates and quadrants of each point.

2-2 Graphing on a Coordinate Plane

Additional Example 2: Graphing Points on a Coordinate Plane

Graph each point on the coordinate plane.

A. A(3, 4)right 3, up 4

B. B(4, 0)right 4, up 0

C. C(–4, 4)left 4, up 4

D. D(–1, –3)left 1, down 3

x

y

A

B

D

C

2-2 Graphing on a Coordinate Plane

Check It Out: Example 2

Graph each point on the coordinate plane.

A. A(2, 4)right 2, up 4

B. B(2, 0)right 2, up 0

C. C(–2, 4)left 2, up 4

D. D(–1, –1)left 1, down 1

x

y

A

BD

C

2-2 Graphing on a Coordinate Plane

Additional Example 3A: Finding Horizontal and Vertical Distances

x

y

= |–6|

Distance = |–2 – (4)| M(2, 6)

Find the distance between each pair of points.

A. K and L

Use the x-coordinates.

0

2468

10

2 4 6 82468

6 4 28

L(4, –2)

N(2, –6)

K(–2, –2)= 6

The points are 6 units apart.

2-2 Graphing on a Coordinate Plane

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

Helpful Hint

2-2 Graphing on a Coordinate Plane

Additional Example 3B: Finding Horizontal and Vertical Distances

x

y

= |12|

Distance = |6 – (–6 )| M(2, 6)

Find the distance between each pair of points.

A. M and N

Use the y-coordinates.

0

2468

10

2 4 6 82468

6 4 28

L(4, –2)

N(2, –6)

K(–2, –2)= 12

The points are 12 units apart.

2-2 Graphing on a Coordinate Plane

Check It Out: Additional Example 3A

x

y

= |–8|

Distance = |–2 – (6)| B(6, 4)

Find the distance between each pair of points.

A. A and B

Use the x-coordinates.

0

2468

10

2 4 6 82468

6 4 28

C(4, –2)

D(4, –8)

A(–2, 4)

= 8The points are 8 units apart.

2-2 Graphing on a Coordinate Plane

Check It Out: Additional Example 3B

x

y

= |6|

Distance = |–2 – (–8)| B(6, 4)

Find the distance between each pair of points.

B. C and D

Use the y-coordinates.

0

2468

10

2 4 6 82468

6 4 28

C(4, –2)

D(4, –8)

A(–2, 4)

= 6The points are 6 units apart.

2-2 Graphing on a Coordinate Plane

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

2-2 Graphing on a Coordinate Plane

Lesson Quiz: Part I

x

y

M

Give the coordinates and quadrant of each point.

1. A

2. C

0

810

8

–8

–8

BA

C

Graph each point on a coordinate plane.

3. L(6, –8)

4. M(0, 8)D

L

(–8,–4), lll

(–4, 6), ll

2-2 Graphing on a Coordinate Plane

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

12 units

x

y

M

0

8

8

–8

–8

BA

C

D

L

2-2 Graphing on a Coordinate Plane

1. 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

2-2 Graphing on a Coordinate Plane

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

2-2 Graphing on a Coordinate Plane

3. Identify the graph of the point A(4, –3).

A. C.

B. D.

Lesson Quiz for Student Response Systems

2-2 Graphing on a Coordinate Plane

4. Identify the graph of the point G(2, 0).

A. C.

B. D.

Lesson Quiz for Student Response Systems

2-2 Graphing on a Coordinate Plane

5. Identify the table for y = 3x – 4 and the graph of each ordered pair.

A. B.

Lesson Quiz for Student Response Systems