graphing lines. i n this section : you will learn to graph ordered pairs you will learn to graph...
TRANSCRIPT
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