GRAPHING LINES. I N THIS SECTION : You will learn to graph ordered pairs You will learn to graph linear equations in two variables You will learn the.

GRAPHING LINES

IN THIS SECTION: You will learn to graph ordered pairs

You will learn to graph linear equations in two variables

You will learn the standard form of a line.

You will learn to graph a line by using the x and y intercepts.

You will verify whether a point lies on a line.

COORDINATE SYSTEM: (X,Y)

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1

2

3

4

5

6

7

-1

-2

-3

-4

-5

-6

-7

x

y

Quadrant I (x,y)

Quadrant II (- x,y)

Quadrant III (- x,- y)

Quadrant IV (x,- y)

Origin(0,0)

A (2,3)

B (-3, 1)

C (-3, -5)

D (2, -6)

PLOTTING POINTS: (X,Y)

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1

2

3

4

5

6

7

-1

-2

-3

-4

-5

-6

-7

x

y

E (0,3)

D (0,-3)

F (3,0)

G (-3,0)

PLOTTING POINTS: (X,Y)

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1

2

3

4

5

6

7

-1

-2

-3

-4

-5

-6

-7

x

y

1) (0,4)2) (-4,3)3) (-4,-5)4) (4,-5)5) (4,3)6) (0,4)Lift your pencil

GRAPH DESIGNS: WHAT DO THESE POINTS MAKE?

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1

2

3

4

5

6

7

-1

-2

-3

-4

-5

-6

-7

x

y

STANDARD FORM OF A LINE:

Linear Equations can be written in standard

form : Ax By C

Examples of equations in standard form :

) 3 4 3 ) 5 2 9a x y b x y

Examples of equations in standard form :

3) 3 4 3 ) 1

n t

4

o

a x y b y x

LINEAR GRAPHS:Do these points lie on the same line?

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1

2

3

4

5

6

7

-1

-2

-3

-4

-5

-6

-7

x

y

A    5,2

B 4, 0   

C 3, 2  

D 1, 4

LINEAR GRAPHS:Do these points lie on the same line?

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1

2

3

4

5

6

7

-1

-2

-3

-4

-5

-6

-7

x

y

A 5, 6   

B 2, 4   

C 1, 2   

D 7, 2

LINEAR GRAPHS:Can you identify three points that lie on

this line?

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1

2

3

4

5

6

7

-1

-2

-3

-4

-5

-6

-7

x

y

LINEAR GRAPHS:Can you identify three points that lie on

this line?

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1

2

3

4

5

6

7

-1

-2

-3

-4

-5

-6

-7

x

y

VERIFYING A POINT ON A LINE:

If you want to verify whether a point lies on the line, then you just need to plug in the values and test whether the equations works out:

Therefore, (2,1) does not lie on this line.

Does 2,1 lie on the line 3 4 7?x y

3 2 4 1 7

6 4 7

10 7

VERIFYING A POINT ON A LINE:

1) Does 2,3 lie on the line 5 7?x y

2) Does 0, 5 lie on the line 3 5?y x

5 2 3 7

10 3 7

13 7

3 5

5 3 0 5

5 5

y x

FINDING THE X AND Y INTERCEPT:

The x-intercept is the point where the line crosses the x-axis.

The y-intercept is the point where the line crosses the y-axis.

1 2 3 4-1-2-3-4

1

2

3

4

-1

-2

-3

-4

x

y

1 2 3 4-1-2-3-4

1

2

3

4

-1

-2

-3

-4

x

y

FINDING THE X AND Y INTERCEPT:

1) 2)

1 2 3 4-1-2-3-4

1

2

3

4

-1

-2

-3

-4

x

y

: 2,0 : 0,2x y : 2,0 : 0, 3x y

1 2 3 4-1-2-3-4

1

2

3

4

-1

-2

-3

-4

x

y

FINDING THE X AND Y INTERCEPT:

3) 4)

Do you notice a pattern with the x and y intercepts?

: 3,0 : 0,2x y : 1,0 : 0, 3x y

1 2 3 4-1-2-3-4

1

2

3

4

-1

-2

-3

-4

x

y

1 2 3 4-1-2-3-4

1

2

3

4

-1

-2

-3

-4

x

y

FINDING THE X AND Y INTERCEPT:

5) 6)

Do you notice a pattern with the x and y intercepts of horizontal and vertical lines?

1 2 3 4-1-2-3-4

1

2

3

4

-1

-2

-3

-4

x

y

1 2 3 4-1-2-3-4

1

2

3

4

-1

-2

-3

-4

x

y

: 2,0 : nonex y : none : 0,3x y

FINDING THE X AND Y INTERCEPT AND GRAPH:1) x-intercept: you set y = 0 and solve

for x.

2) y-intercept: you set x = 0 and solve for y.

5 2 10x y

5 2 10x y

5 2 0 10x 5 10x

2 2,0x

5 0 2 10y 2 10y

5 0,5y

1) Find the and intercepts of 3 4 12.x y x y

int .: 3 4 0 12

3 12

4

x x

x

x

int .: 3 0 4 12

4 12

3

y y

y

y

1 2-1-2-3-4-5

1

2

3

4

-1

-2

-3

-4

x

y

2) Find the and intercepts of 4 3 8.x y x y

int .: 4 3 0 8

4 8

2

x x

x

x

int .: 4 0 3 8

3 8

8 22

3 3

y y

y

y

1 2 3-1-2-3-4-5

1

2

3

4

-1

-2

-3

-4

x

y

CST PREP PROBLEMS:

1) Which point lies on the graph of 3 4 12.x y

A. 0,4 B. 0, 4

C. 0,3 D. 0, 3

CST PREP PROBLEMS:

2) Which point does lie on the graph of

2 6?

not

x y

A. 0,3 B. 2,2

C. 1,5 D. 4,1