1. Graphing on a Coordinate Plane
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. 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

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

5. Vocabulary coordinate plane x-axis y-axis quadrant x-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)
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) (2, 3) move right 2 units move up 3 units (0, 0) originx 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

9. 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

10. 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

11. 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

12. 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

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 –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 –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)